Unitary Jacobi forms and primitive theta functions

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We determined the structure of Jacobi Hecke algebra whose index is a maximal even integral matrix and obtained zonal spherical functions corresponding to irreducible representations of the Hecke algebra, moreover, we showed a relation between a non-commutative Jacobi Hecke algebra and the group ring of a dihedral group (joint work with N. Hashizume). As a global problem, we gave a new system of generators for the ring of paramodular forms of degree 2 and level 2 or 3, by using theta lifts and Klingen Eisenstein series (joint work with Y. Iwahori).