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.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/246