Hecke eigenvalues of Klingen--Eisenstein series of squarefree level

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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 Γ₀⁽ⁿ⁾(N) Hₙ 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 N.