Hecke eigenvalues of Klingen--Eisenstein series of squarefree level

Abstract

We compute the intertwining relation between the Hecke operators and the Siegel lowering operators on Siegel modular forms of arbitrary level $N$ and character $\chi$ by using formulas for the action of the Hecke operators on Fourier expansions. Using an explicit description of the Satake compactification of ${\Gamma }_0^{(n)}(N)\backslash {\mathfrak{H}}_n$ when $N$ is squarefree we extend this to give intertwining relations for each cusp. As an application we give formulas for the action of Hecke operators on the space of Klingen--Eisenstein series of squarefree level $N$, for primes $p\nmid N$.

31 pages