Hecke operators and Hilbert modular forms

2007/11/08 by Gunnells, Paul E., Yasaki, Dan
#11F41 #11F60 #11F75 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0711.1277

Abstract

Let F be a real quadratic field with ring of integers O and with class number 1. Let Gamma be a congruence subgroup of GL₂ (O). We describe a technique to compute the action of the Hecke operators on the cohomology H³ (Gamma; C). For F real quadratic this cohomology group contains the cuspidal cohomology corresponding to cuspidal Hilbert modular forms of parallel weight 2. Hence this technique gives a way to compute the Hecke action on these Hilbert modular forms.

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