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where U, V are mXn real matrices, tr denotes the trace of a corresponding square matrix and G runs through allmXn integral matrices. We write simply 0F,u,v(Z) for the theta series 0f,u,v(Z;0) when 0 is of order 0. For congruence subgroups of SL^{Z) the transformation formulas for theta series of degree 1 associated with F are well known. For example, we can find transformation formulas for theta series of degree 1 in [7],[8],in which multipliers are explicitly determined. Transformation formulas for the theta series 0f,u,v{Z',O) of degree n>l are also established in [1] in the case where F is even and U, V are zero (the condition on U, V is not necessary if 0 is of order 0 [9]). Using these results we can get many examples of Siegel modular forms for congruence subgroups. In this paper we determine a transformation formula for the theta series 0f,u,v(Z;0) associated with a positive integral symmetric matrix F and any real matrices U, V and using this, we get some examples of cusp forms for some congruence subgroups F' of Spn(Z). Cusp forms of weight n + 1 for Fr induce differentialforms of the first kind on the nonsingular model of the modular function fieldwith respect to /''. Our result shows that the geometric genus of the nonsingular model of the modular function fieldwith respect to F' is positive.