Categories and Verbose Output
Example ModForm_Basics (H90E1)
An Illustrative Overview
Example ModForm_Overview (H90E2)
Ambient Spaces
ModularForms (N) : RngIntElt -> ModFrm
ModularForms(N, k) : RngIntElt, RngIntElt -> ModFrm
ModularForms(chars, k) : [GrpDrchElt], RngIntElt -> ModFrm
ModularForms(G) : -> ModFrm
ModularForms(G, k) : -> ModFrm
Example ModForm_Creation-Space (H90E3)
Base Extension
BaseExtend(M, R) : ModFrm, Rng -> ModFrm, Map
BaseExtend(M, phi) : ModFrm, Map -> ModFrm, Map
Example ModForm_BaseExtend (H90E4)
Elements
M . i : ModFrm, RngIntElt -> ModFrmElt
M ! f : ModFrm, . -> ModFrmElt
ModularForm(E) : CrvEll -> ModFrm
Example ModForm_CreationElements (H90E5)
Bases
Basis(M) : ModFrm -> SeqEnum
Example ModForm_Bases (H90E6)
q-Expansions
qExpansion(f) : ModFrmElt -> RngSerPowElt
qExpansion(f, prec) : ModFrmElt, RngIntElt -> RngSerPowElt
PowerSeries(f) : ModFrmElt -> RngSerPowElt
Precision(M) : ModFrm -> RngIntElt
SetPrecision(M, prec) : ModFrm, RngIntElt ->
PrecisionBound(M : parameters) : ModFrm -> RngIntElt
Example ModForm_qExpansion (H90E7)
Example ModForm_WeierstrassPoints (H90E8)
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 ModForm_Arithmetic (H90E9)
Predicates
Degree(f) :ModFrmElt -> RngIntElt
Dimension(M) : ModFrm -> RngIntElt
DirichletCharacters(M) : ModFrm -> [GrpDrchElt]
Eltseq(f) : ModFrmElt -> SeqEnum
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
Level(f) : ModFrmElt -> RngIntElt
Level(M) : ModFrm -> RngIntElt
Weight(f) : ModFrmElt -> RngIntElt
Weight(M) : ModFrm -> RngIntElt
Example ModForm_Predicates (H90E10)
Subspaces
CuspidalSubspace(M) : ModFrm -> ModFrm
EisensteinSubspace(M) : ModFrm -> ModFrm
NewSubspace(M) : ModFrm-> ModFrm
ZeroSubspace(M) : ModFrm -> ModFrm
Example ModForm_Subspaces (H90E11)
Operators
HeckeOperator(M, n) : ModFrm, RngIntElt -> AlgMatElt
HeckePolynomial(M, n : parameters ) : ModFrm, RngIntElt -> RngUPolElt
Example ModForm_HeckePolynomials (H90E12)
Eisenstein Series
EisensteinSeries(M) : ModFrm -> List
IsEisensteinSeries(f) : ModFrmElt -> BoolElt
EisensteinData(f) : ModFrmElt -> Tup
Example ModForm_EisensteinSeries (H90E13)
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 ModForm_Newforms (H90E14)
Labels
Newforms(label) : MonStgElt -> ModFrmElt
Example ModForm_NewformLabeling (H90E15)
Reductions and Embeddings
Reductions(f, p) : ModFrmElt, RngIntElt -> List
pAdicEmbeddings(f, p) : ModFrmElt, RngIntElt -> List
ComplexEmbeddings(f) : ModFrmElt -> List
Example ModForm_ReductionsAndEmbeddings (H90E16)
Congruences
CongruenceGroup(M1, M2, prec) : ModFrm, ModFrm, RngIntElt -> GrpAb
Example ModForm_Congruences (H90E17)
Algebraic Relations
Relations(M, d, prec) : ModFrm, RngIntElt -> SeqEnum
Example ModForm_Relations (H90E18)
Elliptic Curves
ModularForm(E) : CrvEll -> ModFrm
EllipticCurve(f) : ModFrmElt -> CrvEll
Example ModForm_EllipticCurves (H90E19)
Modular Symbols
ModularSymbols(M) : ModFrm -> SeqEnum
ModularSymbols(M, sign) : ModFrm, RngIntElt -> ModSym