Hecke Operators on Drinfeld Cusp Forms

2007/02/25 by Wen-Ching Winnie Li, Li, Wen-Ching Winnie, Yotsanan Meemark +1
Mathematics · #11F52 #20E08 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F52 #msc:20E08

paper · pdf · doi:10.48550/arxiv.math/0702742

28 pages To appear in JNT

arxiv created 2008/04/16 · arxiv updated 2009/12/01

Abstract

In this paper, we study the Drinfeld cusp forms for Γ₁(T) and Γ(T) using Teitelbaum's interpretation as harmonic cocycles. We obtain explicit eigenvalues of Hecke operators associated to degree one prime ideals acting on the cusp forms for Γ₁(T) of small weights and conclude that these Hecke operators are simultaneously diagonalizable. We also show that the Hecke operators are not diagonalizable in general for Γ₁(T) of large weights, and not for Γ(T) even of small weights. The Hecke eigenvalues on cusp forms for Γ(T) with small weights are determined and the eigenspaces characterized.

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