  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.
