Siegel cusp forms of degree 2 are determined by their fundamental\n Fourier coefficients

We prove that a Siegel cusp form of degree 2 for the full modular group is\ndetermined by its set of Fourier coefficients a(S) with 4 det(S) ranging over\nodd squarefree integers. As a key step to our result, we also prove that a\nclassical cusp form of half-integral weight and level 4N, with N odd and\nsquarefree, is determined by its set of Fourier coefficients a(d) with d\nranging over odd squarefree integers, a result that was previously known only\nfor Hecke eigenforms.\n