Eigenvalues of Congruence Covers of Geometrically Finite Hyperbolic Manifolds

Let G = SO(n, 1). for n = 2 and Gamma a geometrically finite Zariski dense subgroup of G which is contained in an arithmetic subgroup of G. Denoting by Gamma(q) the principal congruence subgroup of Gamma of level q, and fixing a positive number lambda(0) strictly smaller than (n - 1)(2)/4, we show that, as q -> infinity along primes, the number of Laplacian eigenvalues of the congruence cover Gamma(q)\H-n smaller than lambda(0) is at most of order [Gamma : Gamma (q)](c) for some c = c(lambda(0)) > 0.