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4 Lists of representations
 4.1 Lists by degree
 4.2 Lists by level
 4.3 Lists of exceptional representations

4 Lists of representations

The degree of a representation is also known as the dimension. The level of the congruent representation determined by the pair \((S,T)\) is equal to the order of \(T\).

We assign to each representation a name according to the conventions of [NW76].

4.1 Lists by degree

4.1-1 SL2IrrepsOfDegree
‣ SL2IrrepsOfDegree( degree )( function )

Returns: a list of records of the form rec(S, T, degree, level, name).

Constructs a list of all irreps of \(\mathrm{SL}_2(\mathbb{Z})\) that have the given degree.

4.1-2 SL2IrrepsOfMaxDegree
‣ SL2IrrepsOfMaxDegree( maximum_degree )( function )

Returns: a list of records of the form rec(S, T, degree, level, name).

Constructs a list of all irreps of \(\mathrm{SL}_2(\mathbb{Z})\) that have at most the given maximum degree.

4.2 Lists by level

4.2-1 SL2IrrepsOfLevel
‣ SL2IrrepsOfLevel( level )( function )

Returns: a list of records of the form rec(S, T, degree, level, name).

Constructs a list of all irreps of \(\mathrm{SL}_2(\mathbb{Z})\) with the given level.

4.3 Lists of exceptional representations

4.3-1 SL2IrrepsExceptional
‣ SL2IrrepsExceptional( arg )( function )

Returns: a list of records of the form rec(S, T, degree, level, name).

Constructs a list of the 18 exceptional irreps of \(\mathrm{SL}_2(\mathbb{Z})\).

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