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

In [6], Shimura introduced modular forms of half-integral weight, their Hecke algebras and their relation to integral weight modular forms via the Shimura correspondence. For modular forms of integral weight, Sturm’s bounds give generators of the Hecke algebra as a module. We also have well-known recursion formulae for the operators $T_{p^{\ell }}$ with $p$ prime. It is the purpose of this paper to prove analogous results in the half-integral weight setting. We also give an explicit formula for how operators $T_{p^{\ell }}$...

We give a geometric interpretation of an arithmetic rule to generate explicit formulas for the Fourier coefficients of elliptic modular forms and their associated Jacobi forms. We discuss applications of these formulas and derive as an example a criterion similar to Tunnel's criterion for a number to be a congruent number.