  We consider modular functions (i.e., the Eisenstein series and Hecke-Maass
forms) for the group PSL(2,Z). We fix a quadratic number field E. This gives
rise to twisted (by a Hecke character of the field E) periods of a modular
function along the torus corresponding to E. We prove meromorphic continuation
for a Dirichlet series generated by these twisted periods.
