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We find linear relations among the Fourier coefficients of modular forms for the group Г0+(p) of genus zero. As an application of these linear relations, we derive congruence relations satisfied by the Fourier coefficients of normalized Hecke eigenforms.

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...

We extend Guerzhoy's Maass-modular grids on the full modular group SL₂(ℤ) to congruence subgroups Γ₀(N) and Γ₀⁺(p).