On Ihara's lemma for degree one and two cohomology over imaginary quadratic fields

Abstract

We prove a version of Ihara's Lemma for degree q=1,2 cuspidal cohomology of the symmetric space attached to automorphic forms of arbitrary weight (k\geq 2) over an imaginary quadratic field with torsion (prime power) coefficients. This extends an earlier result of the author which concerned the case k=2, q=1. Our method here is different and uses results of Diamond and Blasius-Franke-Grunewald. We discuss the relationship of our main theorem to the problem of the existence of level-raising congruences.