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<div class="ChapSects"><a href="chap4_mj.html#X8168FF017B2C0BB2">4 <span class="Heading">Lists of representations</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X80406B597E11D7C6">4.1 <span class="Heading">Lists by degree</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7CC7D26D7E37A1B9">4.1-1 SL2IrrepsOfDegree</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7D5FF1AE85318A70">4.1-2 SL2IrrepsOfMaxDegree</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X78C583957D3FF6ED">4.2 <span class="Heading">Lists by level</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8209AFA6825C44DC">4.2-1 SL2IrrepsOfLevel</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X80400C6D79D4D0D6">4.3 <span class="Heading">Lists of exceptional representations</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X87A4E88F784B5B9A">4.3-1 SL2IrrepsExceptional</a></span>
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<h3>4 <span class="Heading">Lists of representations</span></h3>

<p>The <em>degree</em> of a representation is also known as the <em>dimension</em>. The <em>level</em> of the congruent representation determined by the pair <span class="SimpleMath">\((S,T)\)</span> is equal to the order of <span class="SimpleMath">\(T\)</span>.</p>

<p>We assign to each representation a <em>name</em> according to the conventions of <a href="chapBib_mj.html#biBNW76">[NW76]</a>.</p>

<p><a id="X80406B597E11D7C6" name="X80406B597E11D7C6"></a></p>

<h4>4.1 <span class="Heading">Lists by degree</span></h4>

<p><a id="X7CC7D26D7E37A1B9" name="X7CC7D26D7E37A1B9"></a></p>

<h5>4.1-1 SL2IrrepsOfDegree</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SL2IrrepsOfDegree</code>( <var class="Arg">degree</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: a list of records of the form <code class="code">rec(S, T, degree, level, name)</code>.</p>

<p>Constructs a list of all irreps of <span class="SimpleMath">\(\mathrm{SL}_2(\mathbb{Z})\)</span> that have the given degree.</p>

<p><a id="X7D5FF1AE85318A70" name="X7D5FF1AE85318A70"></a></p>

<h5>4.1-2 SL2IrrepsOfMaxDegree</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SL2IrrepsOfMaxDegree</code>( <var class="Arg">maximum_degree</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: a list of records of the form <code class="code">rec(S, T, degree, level, name)</code>.</p>

<p>Constructs a list of all irreps of <span class="SimpleMath">\(\mathrm{SL}_2(\mathbb{Z})\)</span> that have at most the given maximum degree.</p>

<p><a id="X78C583957D3FF6ED" name="X78C583957D3FF6ED"></a></p>

<h4>4.2 <span class="Heading">Lists by level</span></h4>

<p><a id="X8209AFA6825C44DC" name="X8209AFA6825C44DC"></a></p>

<h5>4.2-1 SL2IrrepsOfLevel</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SL2IrrepsOfLevel</code>( <var class="Arg">level</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: a list of records of the form <code class="code">rec(S, T, degree, level, name)</code>.</p>

<p>Constructs a list of all irreps of <span class="SimpleMath">\(\mathrm{SL}_2(\mathbb{Z})\)</span> with the given level.</p>

<p><a id="X80400C6D79D4D0D6" name="X80400C6D79D4D0D6"></a></p>

<h4>4.3 <span class="Heading">Lists of exceptional representations</span></h4>

<p><a id="X87A4E88F784B5B9A" name="X87A4E88F784B5B9A"></a></p>

<h5>4.3-1 SL2IrrepsExceptional</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SL2IrrepsExceptional</code>( <var class="Arg">arg</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: a list of records of the form <code class="code">rec(S, T, degree, level, name)</code>.</p>

<p>Constructs a list of the 18 exceptional irreps of <span class="SimpleMath">\(\mathrm{SL}_2(\mathbb{Z})\)</span>.</p>


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