Article ID Journal Published Year Pages File Type
6415592 Journal of Number Theory 2014 15 Pages PDF
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 show that modulo T the Hecke algebra has a non-zero semisimple part. In contrast, a well-known theorem of Serre asserts that for classical modular forms the action of Tℓ for any odd prime ℓ is nilpotent modulo 2. After proving the result for Drinfeld modular forms modulo T, we use computations of the Hecke action modulo T to show that certain powers of the Drinfeld modular form h cannot be eigenforms. Finally, we pose a question a positive answer to which will mean that the Hecke algebra that acts on Drinfeld modular forms of full level is not smooth for large weights, which again contrasts the classical situation.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
, ,