  Let E_lambda be a Hilbert space, whose elements are functions spanned by the
eigenfunctions of the Laplace-Beltrami operator associated with an eigenvalue
lambda>0. The norm of elements in this space is given by the Petersson inner
product. In this paper, the trace of Hecke operators T_n acting on the space
E_lambda is computed for congruence subgroups of Gamma_0(N) of square free
level, which may be considered as the analogue of the Eichler-Selberg trace
formula [11] for non-holomorphyic cusp forms of weight zero.
