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algebraic b(mod C/ZT+Z calculation coefficient of q coefficients c(N Cohen's compute conditions at infinity congruence subgroup Corollary to Theorem corresponding CT+d CT+d cusp form defined definition of Jacobi denotes dimension Dirichlet character divisors eigenvalues Eisenstein series equals equation explicitly fact finite follows form of index form of weight forms of half-integral formula Fourier coefficients Fourier development Fourier expansion free module function fundamental discriminant given gives half-integral weight hardcover Hecke eigenforms Hecke operators Heegner points hence integer invariant ISBN isomorphism Jacobi group Jk,m k,m k,m Kohnen's law of Jacobi lower bounds Maass matrices meromorphic mod 2m modular group multiple non-zero obtain odd weight Petersson polynomial prime proof of Theorem prove Theorem qn?r quadratic form quotient r(mod 2m relation replaced resp result ring Siegel modular form space Spezialschar square-free Table Theorem 3.1 theta series transformation law vanishes weak Jacobi form write ZT+Z