Traces of Hecke operators on Drinfeld modular forms for ${\mathrm{GL}}_2({\mathbb{F}}_q[T])$

Abstract

In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case $A={\mathbb{F}}_q[T]$. We deduce closed-form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree. We improve the Ramanujan bound and deduce the decomposition of cusp forms of level ${\Gamma }_0(\mathfrak{p})$ into oldforms and newforms, as conjectured by Bandini-Valentino, under the hypothesis that each Hecke eigenvalue has multiplicity less than $p$.

Numerous updates, including the title. Final version

Cited by in corpus (1)

• Corrigendum to "Isomorphism classes of Drinfeld modules over finite fields"