Siegel Eisenstein Series with Paramodular Level

Starting with a primitive Dirichlet character of conductor $N$, we construct a paramodular Siegel Eisenstein series of level $N^2$ and weight $k\ge 4$. We calculate the Fourier expansion of the holomorphic Siegel modular form thus constructed. The function is a paramodular newform, and its adelization generates an irreducible automorphic representation.