Let F be a real quadratic field with ring of integers O and with class number 1. Let Γ bea congruence subgroup of GL_2(O). We describe a technique to compute the action of the Hecke operators on the cohomology H~3(Γ;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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