In the later day Vaishnava schools Lord Krishna is considered the supreme form of the Lord. This idea is supported by a verse from the Srimad Bhagwatam. The Bhagwatam while describing 24 different Avatar-s of the Lord mentions, when it comes to Krishna,
ete cāṁśa-kalāḥ puṁsaḥ
kṛṣṇas tu bhagavān svayam
mṛḍayanti yuge yuge
All the lists of the incarnations/Avatars mentioned herewith are parts or portions of the Supreme Godhead, but Kṛṣṇa is bhagavan Himself. All these amsas incarnate to protect when the earth is disturbed by the enemies of Indra, that is asuras.
That half phrase – kṛṣṇas tu bhagavān svayam – sealed it for the later schools that Krshna was the greatest manifestation of the Supreme. The word Bhagavan is defined in the Visnu Purana as One who has infinite riches, immeasurable strength, endless fame, absolute wisdom, unmatched beauty, and finally perfect renunciation from everything.
Photo of Lord Krshna from the Banke Bihari temple in Vrndavana.