  Let E_lambda be the Hilbert space spanned by the eigenfunctions of the
non-Euclidean Laplacian associated with a positive discrete eigenvalue lambda.
In this paper, the trace of Hecke operators T_n acting on the space E_lambda is
computed for Hecke congruence subgroups Gamma_0(N) of non-square free level.
This extends the computation of Conrey-Li [2], where only Hecke congruence
subgroups Gamma_0(N) of square free level N were considered.
