  In a series of lectures Selberg introduced a trace formula on the space of
hybrid Maass-modular forms of an irreducible uniform lattice in
$\PSL_2(\bbR)^n$. In this paper we derive the analogous formula for a
non-uniform lattice and use it to study the distribution of elliptic-hyperbolic
conjugacy classes. In particular, for Hilbert modular groups there is a nice
interpretation of these results in terms of class numbers and fundamental units
of quadratic forms over totally real number fields.
