Jacobi forms that characterize paramodular forms
  The Fourier Jacobi expansions of paramodular forms are characterized from among all formal series of Jacobi forms by two conditions on the Fourier coeffcients of the Jacobi forms: a growth condition and a set of linear relations. Examples, both theoretical and computational, indicate that the growth condition may be superfluous. 
Tomoyoshi Ibukiyama, Cris Poor, David S. Yuen
math.NT