  We find nice representatives for the 0-dimensional cusps of the degree $n$
Siegel upper half-space under the action of $\Gamma_0(\stufe)$. To each of
these we attach a Siegel Eisenstein series, and then we make explicit a result
of Siegel, realizing any integral weight average Siegel theta series of
arbitrary level $\stufe$ and Dirichlet character $\chi_L$ modulo $\stufe$ as a
linear combination of Siegel Eisenstein series.
