Art invariant trace formula for rank one lattices

We prove a non-adelic invariant trace formula for rank one lattices. Unlike Arthur's adelic invariant trace formula for groups of general rank, our fo rmula applies to non-congruence lattices, too, and the geometric terms are made explicit. The contribution of the continuous spectrum to the trace is given in terms of certain generalized Hecke operators, and the convergence problem with this contribution is resolved.