Verbose Output
Example ModFrm_Basics (H132E1)
An Illustrative Overview
Example ModFrm_Overview (H132E2)
Ambient Spaces
ModularForms(N) : RngIntElt -> ModFrm
ModularForms(N, k) : RngIntElt, RngIntElt -> ModFrm
ModularForms(eps, k) : GrpDrchElt, RngIntElt -> ModFrm
ModularForms(chars, k) : [GrpDrchElt], RngIntElt -> ModFrm
ModularForms(G) : -> ModFrm
ModularForms(G, k) : -> ModFrm
CuspForms(x) : Any -> ModFrm
Example ModFrm_Creation-Space (H132E3)
Half-integral Weight Forms
HalfIntegralWeightForms(N, w) : RngIntElt, FldRatElt -> ModFrm
HalfIntegralWeightForms(chi, w) : GrpDrchElt, FldRatElt -> ModFrm
HalfIntegralWeightForms(G, w) : GrpPSL2, FldRatElt -> ModFrm
Base Extension
BaseExtend(M, R) : ModFrm, Rng -> ModFrm, Map
BaseExtend(M, phi) : ModFrm, Map -> ModFrm, Map
Example ModFrm_BaseExtend (H132E4)
Elements
M . i : ModFrm, RngIntElt -> ModFrmElt
M ! f : ModFrm, . -> ModFrmElt
ModularForm(E) : CrvEll -> ModFrm
Example ModFrm_CreationElements (H132E5)
Bases
Basis(M) : ModFrm -> SeqEnum
Basis(M, prec) : ModFrm, RngIntElt -> [RngSerPowElt]
PrecisionBound(M : parameters) : ModFrm -> RngIntElt
RModule(M) : ModFrm -> ModTupRng, Map
Example ModFrm_Bases (H132E6)
q-Expansions
qExpansion(f) : ModFrmElt -> RngSerPowElt
Coefficient(f, n) : ModFrmElt, RngIntElt -> RngElt
Precision(M) : ModFrm -> RngIntElt
SetPrecision(M, prec) : ModFrm, RngIntElt ->
Example ModFrm_qExpansion (H132E7)
Example ModFrm_WeierstrassPoints (H132E8)
Arithmetic
f + g : ModFrmElt, ModFrmElt -> ModFrmElt
f + g : ModFrmElt, RngSerPowElt -> RngSerPowElt
f - g : ModFrmElt, ModFrmElt -> ModFrmElt
a * f : RngElt, ModFrmElt -> ModFrmElt
f / a : ModFrmElt, RngElt -> ModFrmElt
f ^ n : ModFrmElt, RngIntElt -> ModFrmElt
f * g : ModFrmElt, ModFrmElt -> ModFrmElt
Example ModFrm_Arithmetic (H132E9)
Predicates
IsAmbientSpace(M) : ModFrm -> BoolElt
IsCuspidal(M) : ModFrm -> BoolElt
IsEisenstein(M) : ModFrm -> BoolElt
IsEisensteinSeries(f) : ModFrmElt -> BoolElt
IsGamma0(M) : ModFrm -> BoolElt
IsGamma1(M) : ModFrm -> BoolElt
IsNew(M) : ModFrm -> BoolElt
IsNewform(f) : ModFrmElt -> BoolElt
IsRingOfAllModularForms(M) : ModFrm -> BoolElt
Example ModFrm_Predicates (H132E10)
Properties
AmbientSpace(M) : ModFrm -> ModFrm
BaseRing(M) : ModFrm -> Rng
Degree(f) : ModFrmElt -> RngIntElt
Dimension(M) : ModFrm -> RngIntElt
DimensionByFormula(M) : ModFrm -> RngIntElt
DimensionByFormula(N, k) : RngIntElt, FldRatElt -> RngIntElt
DirichletCharacters(M) : ModFrm -> [GrpDrchElt]
DirichletCharacter(f) : ModFrmElt -> GrpDrchElt
Eltseq(f) : ModFrmElt -> SeqEnum
Level(f) : ModFrmElt -> RngIntElt
Level(M) : ModFrm -> RngIntElt
Weight(f) : ModFrmElt -> RngIntElt
Weight(M) : ModFrm -> RngIntElt
WeightOneHalfData(H) : ModFrm -> List
Example ModFrm_Properties (H132E11)
Subspaces
ZeroSubspace(M) : ModFrm -> ModFrm
CuspidalSubspace(M) : ModFrm -> ModFrm
EisensteinSubspace(M) : ModFrm -> ModFrm
EisensteinProjection(f) : ModFrmElt -> ModFrmElt
NewSubspace(M) : ModFrm -> ModFrm
DihedralSubspace(M) : ModFrm -> ModFrm
Example ModFrm_Subspaces (H132E12)
Operators
HeckeOperator(M, n) : ModFrm, RngIntElt -> AlgMatElt
HeckeOperator(n,f) : RngIntElt, ModFrmElt -> ModFrmElt
HeckePolynomial(M, n : parameters) : ModFrm, RngIntElt -> RngUPolElt
AtkinLehnerOperator(M, q) : ModFrm, RngIntElt -> AlgMatElt
AtkinLehnerOperator(q,f) : RngIntElt, ModFrmElt -> ModFrmElt
Example ModFrm_HeckePolynomials (H132E13)
Eisenstein Series
EisensteinSeries(M) : ModFrm -> List
IsEisensteinSeries(f) : ModFrmElt -> BoolElt
EisensteinData(f) : ModFrmElt -> Tup
Example ModFrm_EisensteinSeries (H132E14)
Weight Half Forms
WeightOneHalfData(M) : ModFrm -> List
Weight One Forms
DihedralForms(M) : ModFrm -> List
Newforms
NumberOfNewformClasses(M : parameters) : ModFrm -> RngIntElt
Newform(M, i, j : parameters) : ModFrm, RngIntElt, RngIntElt -> ModFrmElt
Newform(M, i : parameters) : ModFrm, RngIntElt -> ModFrmElt
Newforms(M : parameters) : ModFrm -> List
Newforms(I, M) : [Tup], ModFrm -> ModFrm
Example ModFrm_Newforms (H132E15)
Labels
Newforms(label) : MonStgElt -> ModFrmElt
Example ModFrm_NewformLabeling (H132E16)
Reductions and Embeddings
Reductions(f, p) : ModFrmElt, RngIntElt -> List
pAdicEmbeddings(f, p) : ModFrmElt, RngIntElt -> List
ComplexEmbeddings(f) : ModFrmElt -> List
Example ModFrm_ReductionsAndEmbeddings (H132E17)
Congruences
CongruenceGroup(M1, M2, prec) : ModFrm, ModFrm, RngIntElt -> GrpAb
CongruenceGroupAnemic(M1, M2, prec) : ModFrm, ModFrm, RngIntElt -> GrpAb
Example ModFrm_Congruences (H132E18)
Overconvergent Modular Forms
OverconvergentHeckeSeriesDegreeBound(p, N, k, m) : RngIntElt, RngIntElt, RngIntElt, RngIntElt -> RngIntElt
OverconvergentHeckeSeries(p, N, k, m) : RngIntElt, RngIntElt, RngIntElt, RngIntElt -> RngUPolElt
OverconvergentHeckeSeries(p, N, kseq, m) : RngIntElt, RngIntElt, SeqEnum, RngIntElt -> RngUPolElt
Example ModFrm_overconvergent (H132E19)
Algebraic Relations
Relations(M, d, prec) : ModFrm, RngIntElt, RngIntElt -> SeqEnum
Example ModFrm_Relations (H132E20)
Elliptic Curves
ModularForm(E) : CrvEll -> ModFrmElt
Eigenform(E, prec) : CrvEll -> CrvEll, RngIntElt -> RngSerPowElt
EllipticCurve(f) : ModFrmElt -> CrvEll
Example ModFrm_EllipticCurves (H132E21)
Modular Symbols
ModularSymbols(M) : ModFrm -> SeqEnum
ModularSymbols(M, sign) : ModFrm, RngIntElt -> ModSym
Example ModFrm_ModularSymbols (H132E22)
Bibliography
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012