For an odd and squarefree level N, Kohnen proved that there is a canonically defined subspace [...] S κ + 1 2 n e w ( N ) ⊂ S κ + 1 2 ( N ) , and S κ + 1 2 n e w ( N ) and S 2 k n e w ( N ) $S_{\kappa +\frac{1}{2}}^{\mathrm{n}\mathrm{e}\mathrm{w}}\left(N\right)\subset S_{\kappa +\frac{1}{2}}\left(N\right),\text{and}{S}_{\kappa +\frac{1}{2}}^{\mathrm{n}\mathrm{e}\mathrm{w}}\left(N\right)\text{and}{S}_{2k}^{\mathrm{n}\mathrm{e}\mathrm{w}}\left(N\right)$ are isomorphic as modules over the Hecke algebra. Later he gave a formula for the product [...] a g ( m ) a g ( n ) ¯ $a_g\left(m\right)\overline{a_g\left(n\right)}$ of two arbitrary Fourier coefficients of a Hecke eigenform g of halfintegral weight and of level 4N in terms of certain cycle integrals of the corresponding form f of integral weight. To this...