Trace formulae and applications to class numbers

In this paper we compute the trace formula for Hecke operators acting on automorphic forms on the hyperbolic 3-space for the group PSL₂( $\mathcal{O}_K $ ) with $\mathcal{O}_K $ being the ring of integers of an imaginary quadratic number field K of class number H _K > 1. Furthermore, as a corollary we obtain an asymptotic result for class numbers of binary quadratic forms.