Rationality of generating series for the Fourier coefficient of Siegel modular forms of genusn

One proves the rationality of the multiple power series of the form $$sumlimits_{delta _1 geqslant 0} {. . .} sumlimits_{delta _2 geqslant 0} {a(p_1^{delta _1 } . . . p_2^{delta _2 } N)t_1^{delta _1 } . . . t_2^{delta _2 } }$$ where a(...) is the Fourier coefficient of an arbitrary Siegel modular form of genus n?1 relative to a congruence subgroup of the group Sp_n(?), P₁,...,P₇ being a collection of prime numbers, dividing the step of the form.