Divisibility of L-values and the existence of non trivial cohomology classes

We consider a very special class of congruence subgroups of Sl_2(Z[i]) ; for each of these congruence subgroups, the Eisenstein cohomology is essentially described in terms of special values of an L-function attached to a specific Hecke character (which is determined by the subgroup).
We analyze these special values and show that the divisibility of these special values by certain primes ℓ implies that the cohomology of the congruence subgroup contains some non trivial classes. These classes are either cuspidal classes or they are ℓ-torsion classes.