Modular Forms¶
Modular Forms for Arithmetic Groups¶
- Creating spaces of modular forms
- Generic spaces of modular forms
- Ambient spaces of modular forms
- Modular forms with character
- Modular forms for \(\Gamma_0(N)\) over \(\QQ\)
- Modular forms for \(\Gamma_1(N)\) and \(\Gamma_H(N)\) over \(\QQ\)
- Modular forms over a non-minimal base ring
- Submodules of spaces of modular forms
- The cuspidal subspace
- The Eisenstein subspace
- Eisenstein series
- Eisenstein series, optimized
- Elements of modular forms spaces
- Hecke operators on \(q\)-expansions
- Numerical computation of newforms
- The Victor Miller basis
- Compute spaces of half-integral weight modular forms
- Graded rings of modular forms
- \(q\)-expansion of \(j\)-invariant
- \(q\)-expansions of theta series
- Design notes
Modular Forms for Hecke Triangle Groups¶
- Overview of Hecke triangle groups and modular forms for Hecke triangle groups
- Graded rings of modular forms for Hecke triangle groups
- Modular forms for Hecke triangle groups
- Elements of Hecke modular forms spaces
- Elements of graded rings of modular forms for Hecke triangle groups
- Constructor for spaces of modular forms for Hecke triangle groups based on a type
- Functor construction for all spaces
- Hecke triangle groups
- Hecke triangle group elements
- Analytic types of modular forms
- Graded rings of modular forms for Hecke triangle groups
- Modular forms for Hecke triangle groups
- Subspaces of modular forms for Hecke triangle groups
- Series constructor for modular forms for Hecke triangle groups
Quasimodular Forms¶
Miscellaneous Modules (to be sorted)¶
- Dirichlet characters
- The set \(\mathbb{P}^1(\QQ)\) of cusps
- Dimensions of spaces of modular forms
- Conjectural slopes of Hecke polynomials
- Local components of modular forms
- Smooth characters of \(p\)-adic fields
- Type spaces of newforms
- Helper functions for local components
- Eta-products on modular curves \(X_0(N)\)
- The space of \(p\)-adic weights
- Overconvergent \(p\)-adic modular forms for small primes
- Atkin/Hecke series for overconvergent modular forms
- Module of supersingular points
- Brandt modules
- The set \(\mathbb{P}^1(K)\) of cusps of a number field \(K\)
- Hypergeometric motives
- Utility routines for hypergeometric motives
- Algebra of motivic multiple zeta values
- Utilities for Gross-Zagier L-series