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 ${\mathrm{\Gamma }}_0(N)$ over $\mathbf{Q}$
• Modular forms for ${\mathrm{\Gamma }}_1(N)$ and ${\mathrm{\Gamma }}_H(N)$ over $\mathbf{Q}$
• 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

Drinfeld Modular Forms

• Introduction to Drinfeld modular forms
• Graded rings of Drinfeld modular forms
• Elements of Drinfeld modular forms rings

Quasimodular Forms

• Graded quasimodular forms ring
• Elements of quasimodular forms rings

Miscellaneous Modules (to be sorted)

• Dirichlet characters
• The set ${\mathbb{P}}^1(\mathbf{Q})$ 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
• Algebra of motivic multiple zeta values

Indices and Tables

• Index

• Module Index

• Search Page