Arithmetic of Eisenstein series of level T for the function field modular group GL(2,Fq[T])GL(2,Fq[T])

In this paper we study the structure of the algebra of Drinfeld modular forms for the principal congruence subgroup Γ(T)Γ(T) of the full modular group GL(2,Fq[T])GL(2,Fq[T]).To this end and based on work of Cornelissen, we introduce a new class of Eisenstein series and describe their fundamental properties. These so-called modified Eisenstein series allow for a simplification of prior results and are an indispensable tool for future work on Drinfeld modular forms of level T.