- Introduction
- Basics
- Creation Functions
- Ambient Spaces
- ModularSymbols(N) : RngIntElt -> ModSym
- ModularSymbols(N, k) : RngIntElt, RngIntElt -> ModSym
- ModularSymbols(N, k, F) : RngIntElt, RngIntElt, Fld -> ModSym
- ModularSymbols(N, k, sign) : RngIntElt, RngIntElt, RngIntElt -> ModSym
- ModularSymbols(N, k, F, sign) : RngIntElt, RngIntElt, Fld, RngIntElt -> ModSym
- ModularSymbols(eps, k) : GrpDrchElt, RngIntElt -> ModSym
- ModularSymbols(eps, k, sign) : GrpDrchElt, RngIntElt, RngIntElt -> ModSym
- Example ModSym_Creation-Ambient (H142E2)
- Labels
- Creation of Elements
- Bases
- Associated Vector Space
- Degeneracy Maps
- DegeneracyMap(M1, M2, d) : ModSym, ModSym, RngIntElt -> Map
- DegeneracyMatrix(M1, M2, d) : ModSym, ModSym, RngIntElt -> AlgMatElt
- ModularSymbols(M, N') : ModSym, RngIntElt -> ModSym
- M1 !! M2 : ModSym, ModSym -> ModSym
- Example ModSym_Coercion-spaces (H142E9)
- Decomposition
- Subspaces
- Twists
- Operators
- Example ModSym_HeckeOperators (H142E14)
- HeckeOperator(M, n) : ModSym, RngIntElt -> AlgMatElt
- HeckePolynomial(M, n) : ModSym, RngIntElt -> RngUPolResElt
- IntegralHeckeOperator(M, n) : ModSym, RngIntElt -> AlgMatElt
- DualHeckeOperator(M, n) : ModSym, RngIntElt -> AlgMatElt
- AtkinLehner(M, q) : ModSym, RngIntElt -> AlgMatElt
- DualAtkinLehner(M, q) : ModSym, RngIntElt -> AlgMatElt
- StarInvolution(M) : ModSym -> AlgMatElt
- DualStarInvolution(M) : ModSym -> AlgMatElt
- ThetaOperator(M1, M2) : ModSym, ModSym -> Map
- Example ModSym_Operators (H142E15)
- Example ModSym_ThetaOperator (H142E16)
- The Hecke Algebra
- The Intersection Pairing
- q-Expansions
- Special Values of L-functions
- LSeries(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt
- LSeriesLeadingCoefficient(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt, RngIntElt
- RealVolume(M, prec) : ModSym, RngIntElt -> FldPrElt
- MinusVolume(M, prec) : ModSym, RngIntElt -> FldPrElt
- LRatio(M, j : parameters) : ModSym, RngIntElt -> FldRatElt
- LRatioOddPart(M, j) : ModSym, RngIntElt -> FldRatElt
- Example ModSym_LSeries (H142E20)
- Winding Elements
- WindingElement(M) : ModSym -> ModSymElt
- WindingElement(M, i) : ModSym, RngIntElt -> ModSymElt
- TwistedWindingElement(M, i, eps) : ModSym, RngIntElt, GrpDrchElt -> ModSymElt
- WindingLattice(M, j : parameters) : ModSym, RngIntElt -> Lat
- WindingSubmodule(M, j : parameters) : ModSym, RngIntElt -> ModTupFld
- TwistedWindingSubmodule(M, j, eps) : ModSym, RngIntElt, GrpDrchElt -> ModTupFld
- The Associated Complex Torus
- Modular Abelian Varieties
- Elliptic Curves
- Dimension Formulas
- DimensionCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt
- DimensionNewCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt
- DimensionCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt
- DimensionNewCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt
- DimensionCuspForms(eps, k) : GrpDrchElt, RngIntElt -> RngIntElt
- Example ModSym_DimensionFormulas (H142E28)
- Bibliography
V2.28, 13 July 2023