Analytic properties of Euler products for congruence-subgroups of $\operatorname{Sp}_2(\mathbf Z)$

In this paper we prove meromorphic continuation to the entire complex plane and derive a functional equation for the zeta-function $Z_F(s)$ corresponding to a Siegel modular form $F$ which is automorphic for the principal congruence-subgroup of level $q$ in the integral symplectic group $\operatorname{Sp}_2(\mathbf Z)$ of genus $2$ and is an eigenfunction for all of the Hecke operators $T_k(m)$ with index prime to $q$.
Bibliography: 9 titles.