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

TL;DR

This paper proves that all Hecke operators act trivially on the space of ordinary Drinfeld cuspforms of level ^n and weight k, revealing a triviality property in this setting.

Contribution

It establishes the triviality of the Hecke action on ordinary Drinfeld cuspforms at specified levels and weights, a new result in the theory of Drinfeld modular forms.

Findings

Hecke operators act trivially on the space of ordinary Drinfeld cuspforms.

The result holds for all weights k  2 and levels ^n.

The triviality simplifies the structure of these spaces and impacts their arithmetic properties.

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 $k$.