In the Padma Purāṇa, in connection with the glorification of the month of Kārtika, it is stated that devotees pray:
varaṁ deva mokṣaṁ na mokṣāvadhiṁ vā
na cānyaṁ vṛṇe ’haṁ vareśād apīha
idaṁ te vapur nātha gopāla-bālaṁ
sadā me manasy āvirāstāṁ kim anyaiḥ
kuverātmajau baddha-mūrtyaiva yadvat
tvayā mocitau bhakti-bhājau kṛtau ca
tathā prema-bhaktiṁ svakāṁ me prayaccha
na mokṣe graho me ’sti dāmodareha
"Dear Lord, always remembering Your childhood pastimes at Vṛndāvana is better for us than aspiring to merge into the impersonal Brahman. During Your childhood pastimes You liberated the two sons of Kuvera and made them great devotees of Your Lordship. Similarly, I wish that instead of giving me liberation You may award me such devotion unto You."
(Sri Caitanya Caritamrta------1:6:42------purport).

The Cāturmāsya period begins in the month of Āṣāḍha (June-July) from the day of Ekādaśī called Śayanā-ekādaśī, in the fortnight of the waxing moon. The period ends in the month of Kārtika (October-November) on the Ekādaśī day known as Utthānā-ekādaśī, in the fortnight of the waxing moon. This four-month period is known as Cāturmāsya. Some Vaiṣṇavas also observe it from the full-moon day of Āṣāḍha until the full-moon day of Kārtika. That is also a period of four months. This period, calculated by the lunar months, is called Cāturmāsya, but others also observe Cāturmāsya according to the solar month from Śrāvaṇa to Kārtika. The whole period, either lunar or solar, takes place during the rainy season. Cāturmāsya should be observed by all sections of the population. It does not matter whether one is a gṛhastha or a sannyāsī. The observance is obligatory for all āśramas. The real purpose behind the vow taken during these four months is to minimize the quantity of sense gratification. This is not very difficult. In the month of Śrāvaṇa one should not eat spinach, in the month of Bhādra one should not eat yogurt, and in the month of Āśvina one should not drink milk. One should not eat fish or other nonvegetarian food during the month ofKārtika. A nonvegetarian diet means fish and meat. Similarly, masūra dhal and urad dhal are also considered nonvegetarian. These two dhals contain a great amount of protein, and food rich in protein is considered nonvegetarian. On the whole, during the four-month period of Cāturmāsya one should practice giving up all food intended for sense enjoyment.
(Sri Caitanya Caritamrta------2:4:169------purport).

The Dīpāvalī festival takes place on the dark-moon night in the month of Kārtika (October-November). The Rāsa-yātrā, or rāsa dancing of Kṛṣṇa, takes place on the full-moon night of the same month. Utthāna-dvādaśī takes place the day after Ekādaśī in the waxing fortnight of the moon in the same month. All the devotees of Śrī Caitanya Mahāprabhu participated in all these festivals.
(Sri Caitanya Caritamrta------2:15:36------purport).

Śrīla Bhaktivinoda Ṭhākura points out that there are thirty-five items up to the point of observing special vows in the month of Kārtika. To these thirty-five items, another four are added—namely marking tilaka on different parts of the body, writing the names of the Lord all over the body, accepting the Deity's garland and accepting caraṇāmṛta. These four items are understood to be included by Kavirāja Gosvāmī within arcana, worship of the Deity. Although these items are not mentioned here, they are to be added to the previous thirty-five items. Thus the total number becomes thirty-nine. To these thirty-nine should be added five others: association with devotees, chanting the Hare Kṛṣṇa mahā-mantra, reading Śrīmad-Bhāgavatam regularly, residing in Mathurā, the birthplace of Kṛṣṇa, and worshiping the Deity with great respect and veneration. The thirty-nine items plus these five come to a total of forty-four. If we add the previous twenty items to these forty-four, the total number becomes sixty-four. The five items mentioned above repeat previously mentioned items. In the Bhakti-rasāmṛta-sindhu, Śrīla Rūpa Gosvāmī states:
aṅgānāṁ pañcakasyāsya pūrva-vilikhitasya ca
nikhila-śraiṣṭhya-bodhāya punar apy atra śaṁsanam
"The glorification of these five items (association with devotees, chanting the holy name and so on) is to make known the complete superiority of these five practices of devotional service."

The sixty-four items of devotional service include all the activities of the body, mind and senses. Thus the sixty-four items engage one in devotional service in all respects.
(Sri Caitanya Caritamrta------2:22:129------purport).

After visiting Mallāra-deśa, Caitanya Mahāprabhu went to Tamāla-kārtika and then to Vetāpani. There He saw the temple of Raghunātha, Lord Rāmacandra, and passed the night.

Tamāla-kārtika is forty-four miles south of Tirunelveli and two miles south of Aramavallī Mountain. It is located within the jurisdiction of Tovalai. At Tamāla-kārtika is a temple of Subrahmaṇya, or Lord Kārtika, the son of Lord Śiva. Vetāpani, or Vātāpāṇī, is north of Kaila in the Tamil Nadu state. It is also known as Bhūtapaṇḍi and is within the jurisdiction of the Tobala district. It is understood that formerly there was a Deity of Lord Rāmacandra there. Later the Deity was replaced with a deity of Lord Śiva known as Rāmeśvara or Bhūtanātha.
(Sri Caitanya Caritamrta------2:9:225------translation and purport).

The chaste wife must perform such devotional service continuously for one year. After one year passes, she should fast on the full-moon day in the month of Kārttika (October-November).
(Srimad Bhagavatam------6:19:21-------translation).

One should perform the śrāddha ceremony on the Makara-saṅkrānti (the day when the sun begins to move north) or on the Karkaṭa-saṅkrānti (the day when the sun begins to move south). One should also perform this ceremony on the Meṣa-saṅkrānti day and the Tulā-saṅkrānti day, in the yoga named Vyatīpāta, on that day in which three lunar tithis are conjoined, during an eclipse of either the moon or the sun, on the twelfth lunar day, and in the Śravaṇa-nakṣatra. One should perform this ceremony on the Akṣaya-tṛtīyā day, on the ninth lunar day of the bright fortnight of the month of Kārtika, on the four aṣṭakās in the winter season and cool season, on the seventh lunar day of the bright fortnight of the month of Māgha, during the conjunction of Maghā-nakṣatra and the full-moon day, and on the days when the moon is completely full, or not quite completely full, when these days are conjoined with the nakṣatras from which the names of certain months are derived. One should also perform the śrāddha ceremony on the twelfth lunar day when it is in conjunction with any of the nakṣatras named Anurādhā, Śravaṇa, Uttara-phalgunī, Uttarāṣāḍhā or Uttara-bhādrapadā. Again, one should perform this ceremony when the eleventh lunar day is in conjunction with either Uttara-phalgunī, Uttarāṣāḍhā or Uttara-bhādrapadā. Finally, one should perform this ceremony on days conjoined with one's own birth star (janma-nakṣatra) or with Śravaṇa-nakṣatra.
(Srimad Bhagavatam------7:14:20-23-------translation).

Śrīla Viśvanātha Cakravartī Ṭhākura, quoting from the Vaiṣṇava-toṣaṇī of Śrīla Sanātana Gosvāmī, says that the incident of Kṛṣṇa's breaking the pot of yogurt and being bound by mother Yaśodā took place on the Dīpāvalī Day, or Dīpa-mālikā. Even today in India, this festival is generally celebrated very gorgeously in the month of Kārtika by fireworks and lights, especially in Bombay. It is to be understood that among all the cows of Nanda Mahārāja, several of mother Yaśodā's cows ate only grasses so flavorful that the grasses would automatically flavor the milk. Mother Yaśodā wanted to collect the milk from these cows, make it into yogurt and churn it into butter personally, since she thought that this child Kṛṣṇa was going to the houses of neighborhood gopas and gopīs to steal butter because He did not like the milk and yogurt ordinarily prepared.
(Srimad Bhagavatam------10:9:1-2-------purport).

“In the month of Āśvina, the predominating Deity is Padmanābha, and in Kārtika it is Dāmodara. This Dāmodara is different from Rādhā-Dāmodara, the son of Nanda Mahārāja in Vṛndāvana.
(Sri Caitanya Caritamrta------2:20:201------translation).

“(34) One should surrender to Kṛṣṇa in all respects. (35) One should observe particular vows like kārtika-vrata. These are some of the sixty-four important items of devotional service.
(Sri Caitanya Caritamrta------2:22:127------translation).

Similarly, there is a statement in Padma Purāṇa describing the ritualistic function during the month of Kārttika (October-November). During this month, in Vṛndāvana it is the regulative principle to pray daily to Lord Kṛṣṇa in His Dāmodara form. The Dāmodara form refers to Kṛṣṇa in His childhood when He was tied up with rope by His mother, Yaśodā. Dāma means "ropes," and udara means "the abdomen." So mother Yaśodā, being very disturbed by naughty Kṛṣṇa, bound Him round the abdomen with a rope, and thus Kṛṣṇa is named Dāmodara. During the month of Kārttika, Dāmodara is prayed to as follows: "My dear Lord, You are the Lord of all, the giver of all benedictions." There are many demigods, like Lord Brahmā and Lord Śiva, who sometimes offer benedictions to their respective devotees.
(Nectar of Devotion).

(38) In the month of Kārttika (October and November), one should make arrangements for special services. (39) During Janmāṣṭamī (the time of Kṛṣṇa's appearance in this world) one should observe a special service. (40) One should do whatever is done with great care and devotion for the Deity. (41) One should relish the pleasure of Bhāgavatam reading among devotees and not among outsiders. (42) One should associate with devotees who are considered more advanced. (43) One should chant the holy name of the Lord. (44) One should live in the jurisdiction of Mathurā.
Now, the total regulative principles come to an aggregate of sixty-four items.
(Nectar of Devotion).

One of the most important of these ceremonial functions is called Ūrja-vrata. Ūrja-vrata is observed in the month of Kārttika (October-November); especially in Vṛndāvana, there is a specific program for temple worship of the Lord in His Dāmodara form. "Dāmodara" refers to Kṛṣṇa's being bound with rope by His mother, Yaśodā. It is said that just as Lord Dāmodara is very dear to His devotees, so the month known as Dāmodara or Kārttika is also very dear to them.
The execution of devotional service during Ūrja-vrata in the month of Kārttika is especially recommended to be performed at Mathurā. This system is still followed by many devotees. They go to Mathurā or Vṛndāvana and stay there during the month of Kārttika specifically to perform devotional services during this period.

In the Padma Purāṇa it is said, "The Lord may offer liberation or material happiness to a devotee, but after some devotional service has been executed, particularly in Mathurā during the month of Kārttika, the devotees want only to attain pure devotional service unto the Lord." The purport is that the Lord does not award devotional service to ordinary persons who are not serious about it. But even such unserious persons who execute devotional service according to the regulative principles during the month of Kārttika, and within the jurisdiction of Mathurā in India, are very easily awarded the Lord's personal service.
(Nectar of Devotion).

In Śrīmad-Bhāgavatam it is stated that the rāsa dance took place on the full-moon night of the śarat season. From the statements of previous chapters, it appears that the festival of Govardhana-pūjā was performed just after the dark-moon night of the month of Kārttika, and thereafter the ceremony of Bhrātṛ-dvitīyā was performed; then the wrath of Indra was exhibited in the shape of torrents of rain and hailstones, and Lord Kṛṣṇa held up Govardhana Hill for seven days, until the ninth day of the moon. Thereafter, on the tenth day, the inhabitants of Vṛndāvana were talking amongst themselves about the wonderful activities of Kṛṣṇa, and the next day, Ekādaśī, was observed by Nanda Mahārāja. On the next day, Dvādaśī, Nanda Mahārāja went to take a bath in the Ganges and was arrested by one of the men of Varuṇa; then he was released by Lord Kṛṣṇa. Then Nanda Mahārāja, along with the cowherd men, was shown the spiritual sky.
(Krsna Book).

According to the Vaiṣṇava almanac, the twelve months of the year are named according to the twelve Vaikuṇṭha forms of Lord Kṛṣṇa, and these forms are known as the predominating Deities for the twelve months. This calendar begins with the month of Mārgaśīrsa, which is equivalent to late October and early November. The remainder of November is known by Vaiṣṇavas as Keśava. December is called Nārāyaṇa, January is called Mādhava, February is Govinda, March is Viṣṇu, April Śrī Madhusūdana, May Trivikrama, June Vāmana, July Śrīdhara, August Hṛṣīkeśa, September Padmanābha, and early October is known as Dāmodara. (The name Dāmodara was given to Kṛṣṇa when He was bound by ropes by His mother, but the Dāmodara form in the month of October is a different manifestation). Just as the months of the year are known according to the twelve different names of the Supreme Lord, the Vaiṣṇava community marks twelve parts of the body according to these names. For instance, the tilaka mark on the forehead is called Keśava, and on the stomach, breast and arms the other names are also given. These are the same names as those given the months.
(Teachings of Lord Caitanya).

There is a statement in Padma Purāṇa describing the ritualistic function during the month of Kārttika (October-November). During this month, in Vṛndāvana it is the regulative principle to pray daily to Lord Kṛṣṇa in His Dāmodara form. The Dāmodara form refers to Kṛṣṇa in His childhood when He was tied up with rope by His mother, Yaśodā. Dāma means "ropes," and udara means "the abdomen." So mother Yaśodā, being very disturbed by naughty Kṛṣṇa, bound Him round the abdomen with a rope, and thus Kṛṣṇa is named Dāmodara. During the month of Kārttika, Dāmodara is prayed to as follows: "My dear Lord, You are the Lord of all, the giver of all benedictions." There are many demigods, like Lord Brahmā and Lord Śiva, who sometimes offer benedictions to their respective devotees. For example, Rāvaṇa was blessed with many benedictions by Lord Śiva, and Hiraṇyakaśipu was blessed by Lord Brahmā. But even Lord Śiva and Lord Brahmā depend upon the benedictions of Lord Kṛṣṇa, and therefore Kṛṣṇa is addressed as the Lord of all benefactors. As such, Lord Kṛṣṇa can offer His devotees anything they want, but still, the devotee's prayer continues, "I do not ask You for liberation or any material facility up to the point of liberation. What I want as Your favor is that I may always think of Your form in which I see You now, as Dāmodara. You are so beautiful and attractive that my mind does not want anything besides this wonderful form." In this same prayer, there is another passage, in which it is said, "My dear Lord Dāmodara, once when You were playing as a naughty boy in the house of Nanda Mahārāja, You broke the box containing yogurt, and because of that, mother Yaśodā considered You an offender and tied You with rope to the household grinding mortar. At that time You delivered two sons of Kuvera, Nalakūvara and Maṇigrīva, who were staying there as two arjuna trees in the yard of Nanda Mahārāja. My only request is that by Your merciful pastimes You may similarly deliver me."
(Nectar of Devotion).