  Let G=SO(n,1) 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 tends to 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.
