Categories
Example ModSym_Creation (H108E1)
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
DisownChildren(M) : ModSym ->
Example ModSym_Creation-Ambient (H108E2)
Labels
ModularSymbols(s, sign) : MonStgElt, RngIntElt -> ModSym
Example ModSym_Creation-Spaces (H108E3)
Creation of Elements
Example ModSym_Creation-Elements-1 (H108E4)
Example ModSym_RepresentationConversion (H108E5)
M ! x : ModSym, . -> ModSymElt
ConvertFromManinSymbol(M, x) : ModSym, Tup -> ModSymElt
ManinSymbol(x) : ModSymElt -> SeqEnum
Example ModSym_Creation-Elements-2 (H108E6)
Dirichlet Characters
DirichletGroup(N) : RngIntElt -> GrpDrch
DirichletGroup(N,R) : RngIntElt, Rng -> GrpDrch
DirichletGroup(N,R,z,r) : RngIntElt, Rng, RngElt, RngIntElt -> GrpDrch
Elements(G) : GrpDrch -> SeqEnum
KroneckerCharacter(D) : RngIntElt -> GrpDrchElt
KroneckerCharacter(D, R) : RngIntElt, Rng -> GrpDrchElt
Random(G) : GrpDrch -> GrpDrchElt
Ngens(G) : GrpDrch -> RngIntElt
AssignNames( G, S) : GrpDrch, [MonStgElt] ->
Evaluate(x,n) : GrpDrchElt, RngIntElt -> RngElt
IsEven(x) : GrpDrchElt -> BoolElt
IsOdd(x) : GrpDrchElt -> BoolElt
IsTrivial(x) : GrpDrchElt -> BoolElt
BaseExtend(G, R) : GrpDrch, Rng -> GrpDrch
BaseExtend(G, R, z) : GrpDrch, Rng, RngElt -> GrpDrch
x * y : GrpDrchElt, GrpDrchElt -> GrpDrchElt
x ^ n : GrpDrchElt, RngIntElt -> GrpDrchElt
Example ModSym_Dirichlet (H108E7)
Bases
Basis(M) : ModSym -> SeqEnum
IntegralBasis(M) : ModSym -> Lat
Example ModSym_IntegralBasis (H108E8)
Associated Vector Space
VectorSpace(M) : ModSym -> ModTupFld, Map, Map
DualVectorSpace(M) : ModSym -> ModTupFld
Lattice(M) : ModSym -> Lat
Example ModSym_Representation (H108E9)
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 (H108E10)
Decomposition
Decomposition(M, bound : parameters) : ModSym, RngIntElt -> SeqEnum
NewformDecomposition(M : parameters) : ModSym -> SeqEnum
AssociatedNewSpace(M) : ModSym -> ModSym
SortDecomposition(D) : [ModSym] -> SeqEnum
IsIrreducible(M) : ModSym -> BoolElt
M1 lt M2 : ModSym, ModSym -> BoolElt
Example ModSym_Decomposition (H108E11)
Subspaces
CuspidalSubspace(M) : ModSym -> ModSym
IsCuspidal(M) : ModSym -> BoolElt
EisensteinSubspace(M) : ModSym -> ModSym
IsEisenstein(M) : ModSym -> BoolElt
NewSubspace(M) : ModSym-> ModSym
IsNew(M) : ModSym -> BoolElt
NewSubspace(M, p) : ModSym, RngIntElt -> ModSym
Kernel(I, M) : [Tup], ModSym -> ModSym
Complement(M) : ModSym -> ModSym
BoundaryMap(M) : ModSym -> ModMatFldElt
Example ModSym_Subspaces (H108E12)
Example ModSym_BoundaryMap (H108E13)
Operators
Example ModSym_HeckeOperators (H108E14)
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 (H108E15)
Example ModSym_ThetaOperator (H108E16)
The Hecke Algebra
HeckeBound(M) : ModSym -> RngIntElt
SetHeckeBound(M, n) : ModSym, RngIntElt -> RngIntElt
HeckeAlgebra(M : Bound) : ModSym -> AlgMat
DiscriminantOfHeckeAlgebra(M : Bound) : ModSym -> RngIntElt
HeckeEigenvalueRing(M : parameters) : ModSym -> Rng, Map
HeckeEigenvalueField(M) : ModSym -> Fld, Map
Example ModSym_HeckeAlgebra (H108E17)
The Intersection Pairing
IntersectionPairing(x, y) : ModSymElt, ModSymElt -> FldRatElt
Example ModSym_IntersectionPairing (H108E18)
q-Expansions
qEigenform(M, prec) : ModSym, RngIntElt -> RngSerPowElt
qExpansionBasis(M, prec : parameters) : ModSym, RngIntElt -> SeqEnum
qIntegralBasis(M, prec : parameters: Al) : ModSym, RngIntElt -> SeqEnum
SystemOfEigenvalues(M, prec) : ModSym, RngIntElt -> SeqEnum
Example ModSym_qExpansions (H108E19)
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 (H108E20)
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
SubgroupOfTorus(M, x) : ModSym, ModSymElt -> RngIntElt
SubgroupOfTorus(M, s) : ModSym, SeqEnum -> GrpAb
Example ModSym_CuspidalSubgroup (H108E21)
Example ModSym_CuspidalSubgroupTable (H108E22)
ModularKernel(M) : ModSym -> GrpAb
CongruenceGroup(M : parameters) : ModSym -> GrpAb
IntersectionGroup(M1, M2) : ModSym, ModSym -> GrpAb
IntersectionGroup(S) : SeqEnum -> GrpAb
Example ModSym_BSD (H108E23)
The Period Map
PeriodMapping(M, prec) : ModSym, RngIntElt -> Map
Periods(M, prec) : ModSym, RngIntElt -> SeqEnum
ClassicalPeriod(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt
Projection Mappings
RationalMapping(M) : ModSym -> Map
IntegralMapping(M) : ModSym -> Map
Example ModSym_ModularAbVarRational (H108E24)
Modular Degree and Torsion
ModularDegree(M) : ModSym -> RngIntElt
CongruenceModulus(M : parameters) : ModSym -> RngIntElt
TorsionBound(M, maxp) : ModSym, RngIntElt -> RngIntElt
Example ModSym_ModularAbVarArithmetic (H108E25)
Tamagawa Numbers and Orders of Component Groups
ComponentGroupOrder(M, p) : ModSym, RngIntElt -> RngIntElt
TamagawaNumber(M, p) : ModSym, RngIntElt -> RngIntElt
RealTamagawaNumber(M) : ModSym -> RngIntElt
MinusTamagawaNumber(M) : ModSym -> RngIntElt
Example ModSym_ModularAbVarCompGrp (H108E26)
Elliptic Curves
ModularSymbols(E) : CrvEll -> ModSym
Example ModSym_BSD389A (H108E27)
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