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