2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141720Let 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.Number Theory11F41, 11F60, 11F75text