Properties

AmbientSpace(M) : ModFrm -> ModFrm
The full space of modular forms, in which the given space had been created as a subspace.
BaseRing(M) : ModFrm -> Rng
CoefficientRing(M) : ModFrm -> Rng
The ring over which the given space of modular forms was defined.
Degree(f) : ModFrmElt -> RngIntElt
The number of Galois-conjugates of the modular form f over the prime subfield of (the fraction field of) the base ring of f.
Dimension(M) : ModFrm -> RngIntElt
The dimension of the space M of modular forms or half-integral weight forms.

For spaces defined using the ModularForms constructors, the procedure used to obtain the dimension is to count the relevant Eisenstein series, and apply a formula giving the dimension of the relevant space of cusp forms.

DimensionByFormula(M) : ModFrm -> RngIntElt
The dimension of the given space of modular forms or half-integral weight forms (which must be either a full space or the cuspidal subspace of a full space), as given by the formulas in the paper by Cohen and Oesterle (in `Modular Forms in One Variable, VI', Lecture Notes in Math. 627).
DimensionByFormula(N, k) : RngIntElt, FldRatElt -> RngIntElt
DimensionByFormula(chi, k) : GrpDrchElt, FldRatElt -> RngIntElt
DimensionByFormula(N, chi, k) : RngIntElt, GrpDrchElt, FldRatElt -> RngIntElt
    Cuspidal: BoolElt                   Default: false
The dimension of the full space of the modular forms or half-integral weight forms with level N, character chi (taken to be trivial if not specified) and weight k, as given by the formulas in the paper by Cohen and Oesterle (in `Modular Forms in One Variable, VI', Lecture Notes in Math. 627).

If Cuspidal is set to true, then the dimension of the space of cusp forms is returned.

DirichletCharacters(M) : ModFrm -> [GrpDrchElt]
A sequence containing exactly one representative from each Galois-conjugacy class of Dirichlet characters associated to the space of modular forms M.
DirichletCharacter(f) : ModFrmElt -> GrpDrchElt
Suppose f is a newform, created using the Newform command. This returns a Dirichlet character that is, up to Galois conjugacy, the Nebentypus character of f.
Eltseq(f) : ModFrmElt -> SeqEnum
The sequence [a1, ..., an] such that f = a1 g1 + ... + an gn, where g1, ..., gn is the basis of the parent of the modular form f.
Level(f) : ModFrmElt -> RngIntElt
The level of the modular form f.
Level(M) : ModFrm -> RngIntElt
The level of the space of modular forms M.
Weight(f) : ModFrmElt -> RngIntElt
The weight of the modular form f, if it is defined.
Weight(M) : ModFrm -> RngIntElt
The weight of the space M of modular forms.
WeightOneHalfData(H) : ModFrm -> List
A list of tuples describing a basis of the given space of forms of weight 1/2. Each tuple is a pair <f, t>, where t is an integer and f is a Dirichlet character. The tuple <f, t> designates the sum over all integers n of f(n) q(tn2).

Example ModFrm_Properties (H141E11)

We illustrate each of the above properties with some simple computations in M3(Γ1(11)). 
> M := ModularForms(Gamma1(11),3);
> Degree(M.1);
1
> f := Newform(M,1);
> Degree(f);
4
> Dimension(M);
15
> DirichletCharacters(M);
[
    1,
    $.1,
    $.1^2,
    $.1^5
]
> Level(f);
11
> Level(M);
11
> Weight(f);
3
> Weight(M);
3
> Weight(M.1);
3
V2.28, 13 July 2023