Linear relations and congruences for the coefficients of Drinfeld modular forms

Abstract

We find congruences for the t-expansion coefficients of Drinfeld modular forms for \(GL_2 (\mathbb{F}_q [T])\). We give generalized analogies of Siegel’s classical observation on SL 2(ℤ) by determining all the linear relations among the initial t-expansion coefficients of Drinfeld modular forms for \(GL_2 (\mathbb{F}_q [T])\). As a consequence spaces M k 0 are identified, in which there are congruences for the s-expansion coefficients.