Categories
Example ModSym_Creation (H133E1)
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 (H133E2)
Labels
ModularSymbols(s, sign) : MonStgElt, RngIntElt -> ModSym
Example ModSym_Creation-Spaces (H133E3)
Creation of Elements
Example ModSym_Creation-Elements-1 (H133E4)
Example ModSym_RepresentationConversion (H133E5)
M ! x : ModSym, . -> ModSymElt
ConvertFromManinSymbol(M, x) : ModSym, Tup -> ModSymElt
ManinSymbol(x) : ModSymElt -> SeqEnum
Example ModSym_Creation-Elements-2 (H133E6)
Bases
Basis(M) : ModSym -> SeqEnum
IntegralBasis(M) : ModSym -> Lat
Example ModSym_IntegralBasis (H133E7)
Associated Vector Space
VectorSpace(M) : ModSym -> ModTupFld, Map, Map
DualVectorSpace(M) : ModSym -> ModTupFld
Lattice(M) : ModSym -> Lat
Example ModSym_Representation (H133E8)
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 (H133E9)
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 (H133E10)
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 (H133E11)
Example ModSym_BoundaryMap (H133E12)
Twists
IsTwist(M1, M2, p) : ModSym, ModSym, RngIntElt -> BoolElt, GrpDrchElt
IsMinimalTwist(M, p) : ModSym, RngIntElt -> BoolElt, ModSym, GrpDrchElt
Example ModSym_example-twists (H133E13)
Operators
Example ModSym_HeckeOperators (H133E14)
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 (H133E15)
Example ModSym_ThetaOperator (H133E16)
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 (H133E17)
The Intersection Pairing
IntersectionPairing(x, y) : ModSymElt, ModSymElt -> FldRatElt
Example ModSym_IntersectionPairing (H133E18)
q-Expansions
Eigenform(M, prec) : ModSym, RngIntElt -> RngSerPowElt
qExpansionBasis(M, prec : parameters) : ModSym, RngIntElt -> SeqEnum
qIntegralBasis(M) : ModSym -> SeqEnum
SystemOfEigenvalues(M, prec) : ModSym, RngIntElt -> SeqEnum
Example ModSym_qExpansions (H133E19)
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 (H133E20)
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 (H133E21)
Example ModSym_CuspidalSubgroupTable (H133E22)
ModularKernel(M) : ModSym -> GrpAb
CongruenceGroup(M : parameters) : ModSym -> GrpAb
IntersectionGroup(M1, M2) : ModSym, ModSym -> GrpAb
IntersectionGroup(S) : SeqEnum -> GrpAb
Example ModSym_BSD (H133E23)
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 (H133E24)
Modular Degree and Torsion
ModularDegree(M) : ModSym -> RngIntElt
CongruenceModulus(M : parameters) : ModSym -> RngIntElt
TorsionBound(M, maxp) : ModSym, RngIntElt -> RngIntElt
Example ModSym_ModularAbVarArithmetic (H133E25)
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 (H133E26)
Elliptic Curves
ModularSymbols(E) : CrvEll -> ModSym
EllipticCurve(M) : ModSym -> CrvEll
pAdicLSeries(E, p) : CrvEll, RngIntElt -> RngSerPowElt
Example ModSym_BSD389A (H133E27)
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 (H133E28)
Bibliography
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012