On Klingen Eisenstein series with levels

Abstract

We give a representation theoretic approach to the Klingen lift generalizing the classical construction of Klingen Eisenstein series to arbitrary level for both paramodular and Siegel congruence subgroups. Moreover, we give a computational algorithm for describing the one-dimensional cusps of the Satake compactifications for the Siegel congruence subgroups in the case of degree two for arbitrary levels. As an application of the results thus obtained, we calculate the co-dimensions of the spaces of cusp forms in the spaces of modular forms of degree two with respect to Siegel congruence subgroups of levels not divisible by 8.