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arXiv · 1512.09069

Hecke eigenvalues of Klingen--Eisenstein series of squarefree level

Martin J. Dickson
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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 $χ$ by using formulas for the action of the Hecke operators on Fourier expansions. Using an explicit description of the Satake compactification of $Γ_0^{(n)}(N) \backslash \mathfrak{H}_n$ 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 $p \nmid N$.

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Martin J. Dickson. 2015-12-30. Hecke eigenvalues of Klingen--Eisenstein series of squarefree level. https://arxiv.org/abs/1512.09069

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