The Lord’s first expansion is Lord Balarama.  Lord Balarama expands into the first Catur-vyuha.  The Catur-vyuha, Their expansions and the vilasa (pastime) incarnations of the Lord fall under the tad-ekatma category of forms of the Lord.  Tad-ekatma forms resemble the svayam-rupa form with differences.

The Catur-vyuha are categorized as svamsa (sva means ‘own’; and amsa means ‘part’)  or expansions of the Lord.  The Lord’s prabhava expansions divide into vibhava expanions – Vasudeva, Sankarsan, Pradyumna and Aniruddha.  This first Catur-vyuha expands into the 24 vaibhava-vilasa forms of Vishnu, which preside over the Vaikuntha planets [CC M 20.191].  Catur means ‘four’, and vyuha means ‘guard’ or ‘arms’. The word Catur-vyuha means the incarnations of the Lord who have four arms and guard the four directions.

Lord Narayana expands from Sankarsana.  The second Catur-vyuha – Vasudeva, Sankarsana, Pradyumna and Aniruddha –  expands from Narayana.  The purusa-avataras expand from the Sankarsana of the second Catur-vyuha.  There are thus two divisions of avataras in the svamsa category: those coming from Sankarsana ie. the purusa-avataras; and the lila-avataras.