Abstract
There exist two different generalizations of the classical Saito-Kurokawa lifting to modular forms with (square-free) level; one lifting produces modular forms with respect to Γ 0 ( m ), the other one with respect to the paramodular group Γ para ( m ). We shall give an alternative and unified construction of both liftings using group theoretic methods. The construction shows that a single elliptic modular form may in fact have many Saito-Kurokawa liftings. We also obtain precise information about the spin L -function of the resulting Siegel modular forms.
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