HECKE OPERATORS FOR NON-CONGRUENCE SUBGROUPS OF BIANCHI GROUPS

We prove that the action of the Hecke operators on the cohomology of a finite index non-congruence subgroup Gamma of a Bianchi group is essentially the same as the action of Hecke operators on the cohomology groups of (Gamma) over cap, the congruence closure of Gamma. This is a generalization of Atkiri's conjecture, first confirmed in a special case by Serre in 1987 and proved in general by Berger in 1994.