Representation theory of Drinfeld modular forms of level T

This paper expands upon our results for the arithmetic of Drinfeld modular forms of level T [12] by providing an interpretation from a representation theoretic point of view.We identify GL(2,Fq)GL(2,Fq)-modules that arise naturally from the theory of Drinfeld modular forms of level T   with classical GL(2,Fq)GL(2,Fq)-modules. Using the arithmetic of the so-called modified Eisenstein series all isomorphisms are stated explicitly.In particular, we examine the close connection between Drinfeld modular forms of level T   and the theory of symmetric powers of the tautological representation of GL(2,Fq)GL(2,Fq) described in previous work [13].