Tutorial: Computing With Modular Forms Using Magma

Contents, General, Modular Forms, Modular Symbols, Future

General Modular Forms-Related Functionality

Congruence Subgroups

G := Gamma0(11); G

Gamma_0(11)

Gamma_0(11)

Generators(G)

[
[1 1]
[0 1],

[ 3 -2]
[11 -7],

[ 4 -3]
[11 -8]
]

[
[1 1]
[0 1],

[ 3 -2]
[11 -7],

[ 4 -3]
[11 -8]
]

CosetRepresentatives(G);

[
[1 0]
[0 1],

[ 0  1]
[-1  1],

[-1  1]
[-1  0],

[1 0]
[1 1],

[ 0  1]
[-1  2],

[-1  1]
[-2  1],

[1 0]
[2 1],

[ 0  1]
[-1  3],

[-1  1]
[-3  2],

[1 1]
[1 2],

[-1  2]
[-2  3],

[-2  1]
[-3  1]
]

[
[1 0]
[0 1],

[ 0  1]
[-1  1],

[-1  1]
[-1  0],

[1 0]
[1 1],

[ 0  1]
[-1  2],

[-1  1]
[-2  1],

[1 0]
[2 1],

[ 0  1]
[-1  3],

[-1  1]
[-3  2],

[1 1]
[1 2],

[-1  2]
[-2  3],

[-2  1]
[-3  1]
]

Dimension Formulas

DimensionCuspFormsGamma0(11,2)

DimensionCuspFormsGamma1(13,2)

DimensionNewCuspFormsGamma0(100,2)

Dirichlet Characters

G<a> := DirichletGroup(37);
G

Group of Dirichlet characters of modulus 37 over Rational Field

Group of Dirichlet characters of modulus 37 over Rational Field

Order(a)

[a(n) : n in [1..10]]

[ 1, -1, 1, 1, -1, -1, 1, -1, 1, 1 ]

[ 1, -1, 1, 1, -1, -1, 1, -1, 1, 1 ]

Eltseq(a)

[ 18 ]

[ 18 ]

DimensionCuspForms(a,2)

G<a,b> := DirichletGroup(4*37, CyclotomicField(36));
G

Group of Dirichlet characters of modulus 148 over Cyclotomic Field of order 36
and degree 12

Group of Dirichlet characters of modulus 148 over Cyclotomic Field of order 36 and degree 12

Eltseq(b)

[ 0, 1 ]

[ 0, 1 ]