Balarama is neither.
Kṛṣṇa is clearly shown to be Svayam Bhagavān by Bhāgavatām whose feet are
respected hundreds of times by all other scriptures, with the help of other texts
such as Gītā, Gopāla-tāpanī Upaniṣad, and other scriptures. Other Purāṇas also
state what Bhāgavatm states, that Kṛṣṇa is Svayam Bhagavān. For instance
Brahmāṇḍa Purāṇa says that a particular name of Kṛṣṇa is śuka-vāg-amṛtābdhīnduḥ: particular name of Krishna us given as :"the moon arising from the ocean of nectar of Śukadeva’s speech"
Since it has been shown that Kṛṣṇa is Mahā-vāsudeva, it follows that Baladeva is
Mahā-saṅkarṣaṇa. Whatever form Kṛṣna attains, his associates should attain
corresponding forms. Thus it is incorrect to think that Balarāma is some
āveśāvatāra. It is seen by the descriptions of Kṛṣṇa and Balarāma that they are
tāv aṅghri-yugmam anukṛṣya sarīsṛpantau: Kṛṣṇa and Balarāma, with the
strength of their legs, crawled about zigzag in the muddy places of
athānusmṛtya viprās te anvatapyan kṛtāgasaḥ yad viśveśvarayor yācñām
The brāhmaṇas then came to their senses and began to feel great
remorse. They thought, “We have sinned, for we have denied the request
of the two Lords of the universe, who are engaged in spreading human
dadarśa kṛṣṇaṁ rāmaṁ ca vraje go-dohanaṁ gatau: Akrūra then saw Kṛṣṇa
and Balarāma in the village of Vraja, going to milk the cows.
tau rejatū raṅga-gatau mahā-bhujau: the two mighty-armed Lords shone
splendidly in the arena.
In the world, the sun and moon are described together. The sun and Venus are
not described together.
Thus in Hari-vaṁśa, in glorification of Vāsudeva, Kṛṣṇa
and Balarāma are compared to the moon and sun.
dhvaja-vajrāṅkuśāmbhojaiś cihnitair aṅghribhir vrajam śobhayantau
Two exalted personalities beautified the cow pasture with the
impressions of their feet, which bore the marks of the flag, lightning
bolt, elephant goad and lotus. SB 10.38.30
Thus Balarāma has the qualities of Kṛṣṇa, not of Pṛthu and other āveśa forms.
His glory is described:
naitac citraṁ bhagavati hy anante jagad-īśvare ota-protam idaṁ yasmiṁs
tantuṣv aṅga yathā paṭaḥ
My dear Parīkṣit! That Balarāma killed Dhenukāsura is not such a
wonderful thing, considering that he is Bhagavān, the unlimited and
the controller of the entire universe. In him, the entire cosmos rests
as cloth depends on its threads. SB 10.15.35
vāsudeva-kalānantaḥ sahasra-vadanaḥ svarāṭ agrato bhavitā devo hareḥ
The foremost manifestation of Kṛṣṇa is Saṅkarṣaṇa, who is known as
Ananta and Śeṣa with a thousand heads, because he shines with many
forms. Previous to the appearance of Kṛṣṇa, this original Saṅkarṣaṇa
will appear as Baladeva, just to please the Supreme Lord Kṛṣṇa in his
Saṅkarṣaṇa is the first aṁśa (kalā) of Kṛṣṇa, the son of Vasudeva (Vāsudeva).
He comes personal not as an expansion of Saṅkarṣaṇa, for it is said he exists by
himself (svarāṭ). He is devoid of divisions of time and space (anantaḥ).
Yamunā devī says:
**> rāma rāma mahā-bāho na jāne tava vikramam yasyaikāṁśena vidhṛtā jagatī
jagataḥ pate Rāma, Rāma, O mighty-armed one! I cannot know your full
prowess. With a single portion of yourself you hold up the earth, O
Lord of the universe. SB 10.65.28**
Ekāṁśena means “by whose portion called Śeṣa.” Sridhara Svami provides same explanation.
In Ayodhyā-māhātmya in Skanda Purāṇa(22.214.171.124-63), describing the disappearance pastime
of Lakṣmaṇa, it is said:
tataḥ śeṣātmatāṁ yātaṁ lakṣmaṇaṁ satya-saṅgaram | uvāca madhuraṁ
śakraḥ sarvasya ca saḥ paśyataḥ ||
Then while everyone was looking, Indra spoke in a sweet voice to
Lakshmana, who is always true to his promise, and within whom Sesa had
Lakshmana had undergone a merging with Sesa when Lakshmana descended. When work of helping devatas was completed, Sesa
emerged from Lakshmana and went to Patala again, and Lakshmana went to the spiritual world.
indra uvāca -- lakṣmaṇottiṣṭha śīghraṁ tvam ārohasva padaṁ svakam |
deva-kāryaṁ kṛtaṁ vīra tvayā ripu-nisūdana || vaiṣṇavaṁ paramaṁ
sthānaṁ prāpnuhi svaṁ sanātanam | bhavan-mūrtiḥ samāyātā śeṣo'pi
Indra said: Lakṣmaṇa! Please rise up and ascend to your own place
quickly. O brave one, killer of enemies! You have performed godly
tasks. Attain the highest, eternal abode of Viṣṇu which belongs to
you. Your aṁśa Śeṣa with shining hoods has also come.
Further it is stated( 126.96.36.199)
ity uktvā sura-rājendro lakṣmaṇaṁ
sura-saṅgataḥ | śeṣaṁ prasthāpya pātāle bhū-bhāra-dharaṇa-kṣamam ||
lakṣmaṇaṁ yānam āropya pratasthe divam ādarāt ||
Having said this, Indra, the king of the devatās, surrounded by the
devatās, established Śeṣa, who was capable of holding up the weight of
the earth, in Pātāla. He then reverently had Lakṣmaṇa ascend a
vehicle. Indra then returned to Svarga.
In the section of Narayana Armor, it is shown Baladeva is distinct from Sesa and exceeding him in potency
yajñaś ca lokād avatāt kṛtāntād balo gaṇāt krodha-vaśād ahīndraḥ
May Yajña protect me from defamation! May Balarāma protect me from
death! Śeṣa protect me from envious serpents. SB 6.8.18
Here it is shown that Baladeva is different from Śeṣa and has more powers.
Instead of kṛtantāt, sometimes janāntāt (destruction from others) is seen.
Vasudeva equates Balarāma with Kṛṣṇa.
yuvāṁ na naḥ sutau sākṣāt pradhāna-puruṣeśvarau: you are not our sons
but the very Lords of both material nature and its creator
The word sākṣāt in the verse above has greater significance in the argument.
The statements like "The greatly powerful Balarama is a part of Sesa-Naga"(MB 1.67.152) should be considered as
the perception of the sage who spoke it or it is said with the intent to promulgate popular
Sridhara Svami gives such explanation in SB 10.1.2 where Krishna is apparently described as amsa of Vishnu :
tatrāṁśenāvatīrṇasya viṣṇor vīryāṇi śaṁsa naḥ
Sridhara Svami says, "The word aṁśena (as an aṁśa) is said with the intent to promulgate popular belief."
Alternate explanation is amsena means along with Baladeva. Therefore, it can mean Vishnu(Krishna) who descended with His amsa(Baladeva).
Another way to understand such statements is given here:
According to Hari-vaṁśa Upendra appeared as Kṛṣṇa.
idānīṁ nāśa ārabdhaḥ kulasya dvija-śāpa-jaḥ yāsyāmi bhavanaṁ brahmann
etad-ante tavānagha Now due to the brāhmaṇa’s curse, the disappearance
of my family has already begun. O sinless Brahmā, when my family
disappears. I will pay a visit to your abode. SB 11.6.31
Śrīdhara Svāmī explains that the Lord visiting Brahmā’s abode refers to the son
of Vikuṇṭha returning to his abode.(meaning Krishna is avatara of Vikuntha). Sometimes Kṣīrodakaśāyī is said to come as
Kṛṣṇa, sometimes the puruṣa is said to come as Kṛṣṇa, and sometimes Nārāyaṇa
Rṣi is said to come as Kṛṣṇa. And in speaking of Lakṣmaṇa as Balarāma, Rāma
is said to come as Kṛṣṇa. The hair of Nārāyaṇa is said to come as Kṛṣṇa.
Accepting one statement as authoritative, others are thereby denied. However, all these statements are
true.[in as much as they reflect some particular perspective of scripture]. Additionally, because all
of the statements are made in accordance with the speaker's experience and intellectual resolve, they are consistent in meaning.
Various statements become one statement by following the author’s explanation.
It is like resolving the order of ascension through the path of light towards
liberation and through the path of the nāḍīs in Brahma-sūtra 4.3.1.
When Svayam Bhagavān appears all other forms enter him. This is the meaning
whenever these statements occur.
Thus the wise conclude as follows. How is it possible unless they all enter into
Svayam Bhagavān? Some of the aṁśas also appear again, such as Pradyumna.
Kṛṣṇa merged Śiśupāla and Dantavakra (who had fallen from the son of
Vikuṇṭha’s planet in the universe and should return there) into himself since
Vikuṇṭha had also entered into Kṛṣṇa. When his pastimes ended, Vikuṇṭha’s son
entered his own planet Vaikuṇṭha above Brahmaloka with his associates Jaya
vairānubandha-tīvreṇa dhyānenācyuta-sātmatām nītau punar hareḥ pārśvaṁ
jagmatur viṣṇu-pārṣadau These two associates of Lord Viṣṇu—Jaya and
Vijaya—by meditation with intense, continuous hatred of the Lord,
entered Kṛṣṇa, and then went to the side of the Lord as his two
associates. SB 7.1.26
In Hari-vaṁśa, while Garuḍa was killing demons who had stolen
Kṣīrodakaśayī’s crown, Kṛṣṇa appeared on earth. Recovering the crown, and not
seeing Viṣṇu anywhere on the upper planets, Garuḍa offered the crown to Kṛṣṇa
(in whom Viṣṇu had entered) on the top of Gomanta Mountain.
This is similar to accepting the order of ascension on the path of light as the
main element and the order of the nādīs and rays as the secondary element as per
Braham-sūtra 4.3.1. That method should be seen here as well.
That all amsas appear with Krishna is confirmed in:
sva-śānta-rūpeṣv itaraiḥ sva-rūpair abhyardyamāneṣv anukampitātmā
parāvareśo mahad-aṁśa-yukto hy ajo ’pi jāto bhagavān yathāgniḥ Being
compassionate in mind, when his devotees are afflicted by the demons,
Svayam Bhagavān Kṛṣṇa, though not having material birth, appears
within this world along with all his Viṣṇu expansions, since he is the
lord of all forms of God and devatās. SB 3.2.15
He comes endowed with all aṁśas of his great self when he is born (mahadaṁśa-
yuktaḥ). Śruti says mahāntaṁ vibhum ātmānam: he is the great ruler, the
self. (Kaṭha Upaniṣad 1.2.22) mahadvac ca: since mahat does not refer to
mahat-tattva, avyakta cannot refer to pradhāna. (Brahma-sūtra 1.4.7) Or mahat
refers to the aṁśas. “He is endowed with aṁśas like puruṣas which are great.”
Mahat means that their essential nature is greatness as in the phrase loka-nātham
mahad-bhūtam: he is the master of the worlds, the great one. (Viṣṇu-sahasranāma)
Or “He is endowed with aṁśas and their causes which are great.”
Uddhava speaks to Vidura.
Thus, using similar reasoning, Balarama is not avatar of Vishnu or Sesha though such statements are found in scriptures.
ekonaviṁśe viṁśatime vṛṣṇiṣu prāpya janmanī |
rāma-kṛṣṇāv iti bhuvo bhagavān aharad bharam ||
The Lord appeared in the Vṛṣṇi dynasty in the two forms of Balarāma and
Kṛṣṇa as the nineteenth and twentieth avatāras and relieved the burden of
the earth. SB 1.3.23
The word Bhagavān here indicates the direct appearance of Bhagavān, not from
the puruṣa named Aniruddha. The word Bhagavān distinguishes Kṛṣṇa from
others. Kṛṣṇa and Balarāma are both addressed as Bhagavān since Kṛṣṇa is
directly Bhagavān and Balarāma is his direct expansion. They both relieved
earth of its burden. Thus even Balarāma also rejected as an expansion of
Aniruddha since Kṛṣṇa manifests (Vyuha)Vāsudeva and Balarāma manifests Saṅkarṣaṇa.