ON MODULAR FORMS FOR THE PARAMODULAR GROUPS

We present several results on Siegel modular forms of degree 2 with respect to the paramodular group. We propose a theory of new- and oldforms for such modular forms and show that such a theory follows from an analogous local theory, which is available, and several conjectural results on the global spectrum of GSp(4). Examples for paramodular cusp forms are obtained as Saito–Korukawa liftings from elliptic cusp forms for Γ₀(N).