When this form of Krishna takes on a somewhat different aspect, it is called tadekatma-roupa, because it is related to his personal form. The latter can be divided into two other categories, which themselves exhibit many different traits and in turn fall into two groups: prabhava and vaibhava. As for the vila forms, there are countless prabhava-vilas [four-armed forms, which are named differently according to the arrangement of their symbols: mace, disc, lotus, and conch] through which Krishna stands. multiplies in Vasudeva, Sankarsana, Pradyumna and Aniruddha.
The Lord sometimes thinks he is a little shepherd, sometimes an administrator, son of Vasudeva. It is these various ways of thinking of Krishna that we call Entertainment. In reality, its four-armed form does not differ from the so-called two-armed one, although it appears differently in the features of Krishna and Baladeva. As for the aforementioned emanations, Vasudeva, Sankarsana, Pradyumna and Aniruddha, they form the four original emanations, composed of manifestations with four arms. [Krishna is the original source of all divine emanations, the first four of which are Vasudeva, Sankarsana, Pradyumna and Aniduddha. When these four Deities are represented together, Vasudeva and Sankarsana stand in the center, Pradyumna to the right of Sankarsana and Aniruddha to the left of Vasudeva. They are called the four aides-de-camp of Lord Krishna.]
There are countless quadruple emanations on different planets and places, including Dvaraka and Mathoura, India, where they have been manifested from all eternity. From this original quartet emanate the twenty-four main vaibhava-vilas, forms that are named differently according to the arrangement of the symbols they carry in their hands. These four manifestations of Krishna are also present on each of the planets of the spiritual world, planets which are called Narayana-lokas or Vaikountha-lokas. The Lord manifests there in the four-armed form of Narayana, from which emanate the forms of Vasudeva, Sankarsana, Pradyumna and Aniruddha mentioned above. Narayana occupies the central place there, and thus surrounds himself with the four quadruple emanations. Each of these then multiplies into three others with different names, the first of which is Keshava, resulting in a total of twelve forms known by different names depending on the arrangement of the symbols that Narayana holds in her hands. As for the form of Vasudeva, the three manifestations that emanate from it are Keshava, Narayana and Madhava. The three forms of Sankarsana are called Govinda, Visnu and Shri Madhusudane. It should be noted here that this form of Govinda is not that of Nanda Maharaj's son in Vrindavane. Likewise, Pradyumna multiplies into three forms named Trivikram, Vamana and Shridhar, while the three forms of Aniruddha are Hrishikesh, Padmanabhe and Damodar.
The different forms of Krishna are thus present in our galaxy and in all the others for the pleasure of his devotees. Indeed, the latter do not originate in India, but in all parts of the world. Even when they have forgotten their real identity, these forms come into being for their satisfaction as well as to restore devotional service and perform other activities of vital importance to the Lord God. Some of these forms are Avatars mentioned in the original holy scriptures.