Fourier coefficients of the Siegel Eisenstein series of degree 2 with odd prime level, corresponding to the middle cusp

Abstract

Let p be an odd prime. In this paper we compute the Fourier coefficients of the Siegel Eisenstein series of degree 2, level p with the trivial or the quadratic character, associated to a certain cusp. For that we need to define the p-factor of the special type of Siegel series with character.