  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 $p \nmid N$.
