Abstract
We find nice representatives for the 0-dimensional cusps of the degree n Siegel upper half-space under the action of $$\Gamma _0(\mathcal N )$$ . 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 $$\mathcal N $$ and Dirichlet character $$\chi _{_L}$$ modulo $$\mathcal N $$ as a linear combination of Siegel Eisenstein series.
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