Integral cohomology of certain Picard modular surfaces

Let Γ¯ be the Picard modular group of an imaginary quadratic number field k and let D be the associated symmetric space. Let Γ⊂Γ¯ be a congruence subgroup. We describe a method to compute the integral cohomology of the locally symmetric space Γ\D. The method is implemented for the cases k=Q(i) and k=Q(−3), and the cohomology is computed for various Γ.