Hecke operators and Hilbert modular forms

Abstract

Let F be a real quadratic field with ring of integers and with class number 1. Let Γ be a congruence subgroup of . We describe a technique to compute the action of the Hecke operators on the cohomology . 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. © 2008 Springer-Verlag Berlin Heidelberg.