Hecke eigenforms for meromorphic cusp forms

In this paper, we construct Hecke eigenforms for two families of quotient spaces of meromorphic cusp forms on SL₂(Z) SL 2 ( Z ) . We show that each quotient space in the first (resp. second family) is isomorphic as a Hecke module to the space S₂ₖ S 2 k (resp. M₂ₖ M 2 k ) of cusp forms (resp. holomorphic modular forms) of the same weight on SL₂(Z) SL 2 ( Z ) .