Small eigenvalues of automorphic Laplacians in spaces of cusp forms

The Yang-Yau inequality for $\lambda$, of the Laplace operator of a compact Riemann surface is adapted to the case of a Fucahian group of the first kind. For certain subgroups of the modular group $PSL(2, \mathbb Z)$ be occurenoe of cuspidal representations of complementary series in the regular representations of $PSL(2, \mathbb R)$ is proved. The degree of any non-constant meromorphic function which is automorphic with respect to a congruence subgroup $\Gamma$ of $PSL(2, \mathbb Z)$, is estimated from below in terms of index of $\Gamma$ in $PSL(2, \mathbb Z)$ only.