Hecke operators and Hilbert modular forms

Details Hecke operators and Hilbert modular forms Hecke operators and Hilbert modular forms

2007-11-08

arxiv.org/abs/0711.1277v1

Mathematics

Number Theory

Scientific paper

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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