Abstract
In this paper, we study the Drinfeld cusp forms for Γ 1 ( 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 Γ 1 ( 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 Γ 1 ( 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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