On the action of Hecke operators on Drinfeld modular forms

TL;DR

This paper analyzes the structure of Hecke operators on Drinfeld modular forms, revealing the semisimple part of the Hecke algebra and providing insights into eigenforms and algebraic properties at full level modulo T.

Contribution

It explicitly determines the semisimple structure of the Hecke algebra on Drinfeld modular forms and explores non-eigenform forms and algebra smoothness conjectures.

Findings

Identified the semisimple part of the Hecke algebra modulo T

Discovered Drinfeld modular forms that are not eigenforms

Conjectured non-smoothness of the Hecke algebra for large weights

Abstract

In this paper we determine the explicit structure of the semisimple part of the Hecke algebra that acts on Drinfeld modular forms of full level modulo T . We use computations of the Hecke action modulo T to find Drinfeld modular forms that cannot be eigenforms. Finally, we conjecture that the Hecke algebra that acts on Drinfeld modular forms of full level is not smooth for large weight.