  H. Aoki showed that any symmetric formal Fourier-Jacobi series for the
symplectic group Sp_2(Z) is the Fourier-Jacobi expansion of a holomorphic
Siegel modular form. We prove an analogous result for vector valued symmetric
formal Fourier-Jacobi series, by combining Aoki's theorem with facts about
vector valued modular forms. Recently, this result was also proved
independently by M. Raum using a different approach. As an application, by
means of work of W. Zhang, modularity results for special cycles of codimension
2 on Shimura varieties associated to orthogonal groups can be derived.
