svyam-rupa, tad-ekatma-rupa, avesa-nama/prathamei-rupe rahena bhagavan
‘The Supreme Personality of Godhead exists in three principal forms – svyam-rupa, tad-ekatma rupa and avesa-rupa‘ [Caitanya-caritamrta Madhya-lila 20.165]
The Sanskrit word avatara means ‘one who descends from the Kingdom of God’ into the material creation [see: CC Madhya-Lila 20.263-64]. The word avatara usually applies to the Supreme Personality of Godhead. Svyam-rupa bhagavan, the original form of the Lord, is avatari or ‘the source of all incarnations’. This form is not dependent on any others [Laghu-bhagavatamrta (LB) 1.12].
Caitanya-caritamrita explains: ‘svyam rupa’ ‘svyam-prakash’-dui rupe sphurti/ ‘svyam-rupe’-eka ‘krsna vraje gopa murti’. Translation: ‘Krsna reveals Himself in two forms, as svyam-rupa (His own form) and svyam-prakash (His own manifestation). Svyam-rupa is Krishna Himself in Vrindavana, in the figure of a cowherd boy’ [CC M 20.166].
The direct expansions of the Lord’s svyam-rupa are called svyam-prakash (prakash means ‘the same’). These are direct expansions of the Lord and appear exactly the same eg. when the Lord expanded Himself into numerous forms during the rasa-dance. In the case of Lord Balarama, the first direct expansion of Krishna, the only difference from the original form is bodily colour.
The tad-ekatma-rupa is abheda ie. non-different to the svyam-rupa. The tad-ekatma-rupa, however, appears to differ from the svyam-rupa by form, activities and qualities. Visvanatha Cakravarti Thakur gives the example of the moon. The moon, occluded by shadow, is the same full moon. It only appears to be different. Those forms of Krishna, therefore, which appear different from His original form are still manifestations of that original form.
The tad-ekatma form of the Lord is not the same as the svyam-prakash forms of the Lord. The svyam-prakash forms are, in essence, the same as the svayama-rupa. The tad-ekatma-rupa consists of both svamsa incarnations ( expansions of expansions of the svyama form) and vilasa forms (forms that differ in appearance from the svyama-rupa) [CC M.20.174P, Srila Prabhupada cites Bhaktivinoda Thakur]. Srila Prabhupada explains in CC Madhya-lila 20.185 Purport: ‘When a form of Krishna is nondifferent from the original form but is less important and exhibits less potency it is called svamsa‘. Svamsa forms include the purusa-avataras and avataras like Matsya, Kurma, Varaha and Nrsimhadeva. Vilasa incarnations are categorised as prabhava (ie. the catur-vyuha) and vaibhava (the 24 forms of Vishnu emanating from the catur-vyuha, including the second catur-vyuha).
Avesa-rupa refers to ’empowered forms of the Lord’ ie. the Lord manifesting his energies or qualities through powerful jivas or living entities. Examples of these are Narada, Prithu and Brahma. The avesa-avataras are living entities. The use of the word avatara, therefore, is secondary.
The Lords forms are unlimited. Even Ananta Sesa – Lord Vishnu appearing with a hood of many serpent-like heads – cannot fully describe the manifestation of the Lord’s unlimited forms. This is confirmed in Srimad Bhagavatam: avatara hy asankhyeya/hareh sattva-nidher dvijah/yathavidasinah kulyah/sarasah syuh sahasrasah: ‘O brahmanas, the incarnations of the Lord are innumerable, like rivulets flowing from inexhaustible sources of water’ [SB 1.3.26].
HARE KRISHNA 
16 March, 2011 at 1:43 pm
‘Therefore one must learn about Krsna from the acaryas. ‘Acaryavah puruso veda’: one who follows the path of the acaryas knows things as they are. Such a person can know Krsna as He is, at least to some extent, and as soon as one understands Krsna (‘janma karma ca me divyam evam yo vetti tattvatah), one is liberated from material bondage (‘tyaktva deham punar janma/naiti mam eti so ‘rjuna).’
SB 10.13.19 Purport
16 March, 2011 at 1:48 pm
Glossary
Svamsa (sva – own; amsa – part): ‘When a form of Krsna is non-different from the original form but is less important and exhibits less potency, it is called ‘svamsa” [Laghu-bhagavatamrta 1.15; cf. Caitanya-caritamrita Madhya Lila 20, p.185]. ‘Svamsa’ incarnations are ‘avataras’ of Krishna that enter the material world.
23 March, 2011 at 4:15 am
Rupa Goswami defines ‘prakash-vigrahas’ and ‘vilasa-vigrahas’ in ‘Laghu-bhagavatamrita’:
‘If numerous forms, all equal in Their features, are displayed simultaneously, such forms are called ‘prakash-vigrahas’ of the Lord’ – CC Adi 75
‘But when the numerous forms are slightly different from one another, they are called ‘vilasa-vigrahas” – CC Adi 76
25 March, 2011 at 9:44 am
”svayam-rupa’ ‘svyam-prakasa’-dui rupe sphurti/svyam-rupe – eka ‘krsna’ vraje gopa-murti’
‘Krsna reveals Himself in two forms, as ‘svyam-rupa’ (His own form) and svyam-prakasa (His own manifestation). ‘Svyam-rupa’ is Krsna Himself in Vrindavan in the figure of a cowherd boy’ [CC M 20.166]
Krsna is lila-purusottama. Balarama is His first expansion.
6 May, 2011 at 6:00 pm
‘Sri Krishna is sattva-nidhi, the original source of all sattva, which Srila Sanatana Goswami defines here as “compassion”. The Lord expresses this compassion by descending to the material world in numerous forms, which are all secondary “rivulets” flowing from Him, their “inexhuastible source”‘ [Brihad-Bhagavatamrtam 1.3.9P]
‘Narayana means the Personality of Godhead who casts His merciful glance((ayate) on the multitude of living beings (nara). By this glance He bestows the potencies of knowledge and action, thus engaging the jivas in useful and sanctifying activities. Only Lord Narayana equals Krishna in some respects; the secondary expansions of Godhead do not even begin to equal Krishna’ [BB 1.5.13P], and:
‘The creative Purusa forms of Visnu is glorified as the source of all avataras: etan nanavataranam/nidhanam bijam avyayam –
“This Purusa is the source and indestructible seed of multifarious incarnations within the universe” (Bhagavatam 1.3.5). But in spite of belonging to the exclusive category of avatari (“source of incarnations”), the Purusa Visnu does not display all-attractive, supremely sweet pleasure pastimes like Sri Krsna. Only Narayana in Vaikunth exhibits personal pastimes somewhat resembling Krishna’s, but these lilas of Vaikuntha cannot match the charm and intimacy of Krishna’s sports in Goloka Vrindavana’