Modular Forms#

Module List#

Creating Spaces of Modular Forms
- CuspForms()
- EisensteinForms()
- ModularForms()
- ModularForms_clear_cache()
- Newform()
- Newforms()
- canonical_parameters()
- parse_label()
Generic spaces of modular forms
- ModularFormsSpace
- contains_each()
- is_ModularFormsSpace()
Ambient Spaces of Modular Forms
- ModularFormsAmbient
Modular Forms with Character
- ModularFormsAmbient_eps
Modular Forms for \(\Gamma_0(N)\) over \(\QQ\)
- ModularFormsAmbient_g0_Q
Modular Forms for \(\Gamma_1(N)\) and \(\Gamma_H(N)\) over \(\QQ\)
- ModularFormsAmbient_g1_Q
- ModularFormsAmbient_gH_Q
Modular Forms over a Non-minimal Base Ring
- ModularFormsAmbient_R
Submodules of spaces of modular forms
- ModularFormsSubmodule
- ModularFormsSubmoduleWithBasis
The Cuspidal Subspace
- CuspidalSubmodule
- CuspidalSubmodule_R
- CuspidalSubmodule_eps
- CuspidalSubmodule_g0_Q
- CuspidalSubmodule_g1_Q
- CuspidalSubmodule_gH_Q
- CuspidalSubmodule_level1_Q
- CuspidalSubmodule_modsym_qexp
- CuspidalSubmodule_wt1_eps
- CuspidalSubmodule_wt1_gH
The Eisenstein Subspace
- EisensteinSubmodule
- EisensteinSubmodule_eps
- EisensteinSubmodule_g0_Q
- EisensteinSubmodule_g1_Q
- EisensteinSubmodule_gH_Q
- EisensteinSubmodule_params
- cyclotomic_restriction()
- cyclotomic_restriction_tower()
Eisenstein Series
- compute_eisenstein_params()
- eisenstein_series_lseries()
- eisenstein_series_qexp()
Eisenstein Series (optimized compiled functions)
- Ek_ZZ()
- eisenstein_series_poly()
Elements of modular forms spaces
- EisensteinSeries
- GradedModularFormElement
- ModularFormElement
- ModularFormElement_elliptic_curve
- ModularForm_abstract
- Newform
- delta_lseries()
- is_ModularFormElement()
Hecke Operators on \(q\)-expansions
- hecke_operator_on_basis()
- hecke_operator_on_qexp()
Numerical computation of newforms
- NumericalEigenforms
- support()
The Victor Miller Basis
- delta_qexp()
- victor_miller_basis()
Compute spaces of half-integral weight modular forms
- half_integral_weight_modform_basis()
Graded rings of modular forms
- ModularFormsRing
q-expansion of j-invariant
- j_invariant_qexp()
q-expansions of Theta Series
- theta2_qexp()
- theta_qexp()

Design Notes#

Design Notes

Indices and Tables#