ON SAITO-KUROKAWA DESCENT FOR CONGRUENCE SUBGROUPS

The conjecture made by H. Saito and N. Kurokawa states the existence o f a ''lifting'' from the space of elliptic modular forms of weight 2k - 2 (for the full modular group) to the subspace of the space of Siege l modular forms of weight k (for the full Siegel modular group) which is compatible with the action of Hecke operators. (The subspace is the so called ''Maass spezialschar'' defined by certain identities among Fourier coefficients). This conjecture was proved (in Darts) by H. Maa ss, A.N. Andrianov and D. Zagier. The purpose of this paper is to prov e a generalised version of the conjecture for cusp forms of odd square free level.