Congruences of Siegel Eisenstein series of degree two

In this paper we study congruences between Siegel Eisenstein series and Siegel cusp forms for Sp4(Z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{Sp}_4(\mathbb {Z})$$\end{document}.