jsMath

# Tutorial: Computing With Modular Forms Using Magma

Contents, General, Modular Forms, Modular Symbols, Future

# 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)`
 `1` `1`
`DimensionCuspFormsGamma1(13,2)`
 `2` `2`
`DimensionNewCuspFormsGamma0(100,2)`
 `1` `1`

# 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)`
 `2` `2`
`[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)`
 `2` `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 ]`