Predicates

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.

DirichletCharacters(M) : ModFrm -> [GrpDrchElt]

A sequence whose elements give one representative from each Galois-conjugacy class of Dirichlet characters associated to M.

Eltseq(f) : ModFrmElt -> SeqEnum

The sequence [a_1, ..., a_n] such that f = a_1 g_1 + ... + a_n g_n, where g_1, ..., g_n is the basis of the parent of f.

IsAmbientSpace(M) : ModFrm -> BoolElt

Returns true if and only if M is an ambient space. Ambient spaces are those space constructed in Section Ambient Spaces.

IsCuspidal(M) : ModFrm -> BoolElt

Returns true if M is contained in the cuspidal subspace of the ambient space.

IsEisenstein(M) : ModFrm -> BoolElt

Returns true if M is contained in the Eisenstein subspace of the ambient space.

IsEisensteinSeries(f) : ModFrmElt -> BoolElt

Returns true if f is an Eisenstein newform or was computed using the intrinsic EisensteinSeries. (See Section Eisenstein Series.)

IsGamma0(M) : ModFrm -> BoolElt

Returns true if M is a space of modular forms for Gamma_0(N).

IsGamma1(M) : ModFrm -> BoolElt

Returns true if M is a space of modular forms for Gamma_1(N). (For efficiency purposes, if you create a space using the ModularForms(chars,k) constructor, and chars consists of all mod N Dirichlet characters, then IsGamma1 will still be false.)

IsNew(M) : ModFrm -> BoolElt

Returns true if M is contained in the new subspace of the ambient space.

IsNewform(f) : ModFrmElt -> BoolElt

Returns true if f was created using Newforms. (Sometimes true in other cases in which f is obviously a newform. In number theory, "newform" means "normalized eigenform that lies in the new subspace".)

IsRingOfAllModularForms(M) : ModFrm -> BoolElt

Returns true if and only if M is the ring of all modular forms over a given ring.

Level(f) : ModFrmElt -> RngIntElt

The level of f.

Level(M) : ModFrm -> RngIntElt

The level of 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.

Example ModForm_Predicates (H90E10)

> 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
]
> IsAmbientSpace(M);
true
> IsAmbientSpace(CuspidalSubspace(M));
false
> IsCuspidal(M);
false
> IsCuspidal(CuspidalSubspace(M));
true
> IsEisenstein(CuspidalSubspace(M));
false
> IsEisenstein(EisensteinSubspace(M));
true
> IsGamma1(M);
true
> IsNew(M);
true
> IsNewform(M.1);
false
> IsNewform(f);
true
> IsRingOfAllModularForms(M);
false
> Level(f);
11
> Level(M);
11
> Weight(f);
3
> Weight(M);
3
> Weight(M.1);
3