Hecke operators and Hilbert modular forms

Authors:
Paul E. Gunnells;Dan Yasaki
Affiliations:
University of Massachusetts Amherst, Amherst, MA;University of Massachusetts Amherst, Amherst, MA
Venue:
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Year:
2008

Citing 2
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Abstract

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