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arXiv · 0711.1277

Hecke operators and Hilbert modular forms

Paul E. Gunnells·Dan Yasaki
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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 GL_2 (O). We describe a technique to compute the action of the Hecke operators on the cohomology H^3 (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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Paul E. Gunnells, Dan Yasaki. 2007-11-08. Hecke operators and Hilbert modular forms. https://arxiv.org/abs/0711.1277

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