On Level p Siegel Cusp Forms of Degree Two

In the previous paper 1 , the second and the third authors introduced a simple construction of a Siegel cusp form of degree 2. This construction has an advantage because the Fourier coefficients are explicitly computable. After this work was completed, Kikuta and Mizuno proved that the p-adic limit of a sequence of the aforementioned cusp forms becomes a Siegel cusp form of degree 2 with level p. In this paper, we give an explicit description of the Fourier expansion of such a form. This result shows that the cusp form becomes a nonzero cusp form of weight 2 on Γ0 p if p > 7 and p ≡ 3 mod 4 .