ON IHARA'S LEMMA FOR DEGREE ONE AND TWO COHOMOLOGY OVER IMAGINARY QUADRATIC FIELDS

KRZYSZTOF KLOSIN
2013 International Journal of Number Theory  
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 ≥ 2) over an imaginary quadratic field with torsion (p-power) coefficients. This extends an earlier result of the author [9] which concerned the case k = 2, q = 1. Our method is different from [9] and uses results of Diamond [4] and Blasius-Franke-Grunewald [2]. We discuss the relationship of our main theorem to the problem of the existence of
more » ... the existence of level-raising congruences. 0 2010 Mathematics subject classification 11F33 (primary), 11F75 (secondary).
doi:10.1142/s1793042113500425 fatcat:gpuzgsaqxba2lnez6jx3gafw5a