Triviality of the Hecke action on ordinary Drinfeld cuspforms of level $\Gamma_1(t^n)$

Abstract

Let $k\geq 2$ and $n\geq 1$ be any integers. In this paper, we prove that all Hecke operators act trivially on the space of ordinary Drinfeld cuspforms of level $\Gamma_1(t^n)$ and weight $k$.