<!-- This is an automatically generated file. -->
<Chapter Label="Chapter_Lists">
<Heading>Lists of representations</Heading>
<P/>
The <Emph>degree</Emph> of a representation is also known as the <Emph>dimension</Emph>.
The <Emph>level</Emph> of the congruent representation determined by the pair <Math>(S,T)</Math> is equal to the order of <Math>T</Math>.
<P/>
We assign to each representation a <Emph>name</Emph> according to the conventions of <Cite Key="NW76"/>.
<Section Label="Chapter_Lists_Section_Degree">
<Heading>Lists by degree</Heading>
<ManSection>
<Func Arg="degree" Name="SL2IrrepsOfDegree" />
<Returns>a list of records of the form <Code>rec(S, T, degree, level, name)</Code>.
</Returns>
<Description>
Constructs a list of all irreps of <Math>\mathrm{SL}_2(\mathbb{Z})</Math>
that have the given degree.
</Description>
</ManSection>
<ManSection>
<Func Arg="maximum_degree" Name="SL2IrrepsOfMaxDegree" />
<Returns>a list of records of the form <Code>rec(S, T, degree, level, name)</Code>.
</Returns>
<Description>
Constructs a list of all irreps of <Math>\mathrm{SL}_2(\mathbb{Z})</Math>
that have at most the given maximum degree.
</Description>
</ManSection>
</Section>
<Section Label="Chapter_Lists_Section_Level">
<Heading>Lists by level</Heading>
<ManSection>
<Func Arg="level" Name="SL2IrrepsOfLevel" />
<Returns>a list of records of the form <Code>rec(S, T, degree, level, name)</Code>.
</Returns>
<Description>
Constructs a list of all irreps of <Math>\mathrm{SL}_2(\mathbb{Z})</Math>
with the given level.
</Description>
</ManSection>
</Section>
<Section Label="Chapter_Lists_Section_Exceptions">
<Heading>Lists of exceptional representations</Heading>
<ManSection>
<Func Arg="arg" Name="SL2IrrepsExceptional" />
<Returns>a list of records of the form <Code>rec(S, T, degree, level, name)</Code>.
</Returns>
<Description>
Constructs a list of the 18 exceptional irreps of <Math>\mathrm{SL}_2(\mathbb{Z})</Math>.
</Description>
</ManSection>
</Section>
</Chapter>
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