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<div class="ChapSects"><a href="chap1_mj.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X8360C04082558A12">1.1 <span class="Heading">Installation</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X86A9B6F87E619FFF">1.2 <span class="Heading">Usage</span></a>
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<h3>1 <span class="Heading">Introduction</span></h3>

<p>This package, <code class="code">SL2Reps</code>, provides methods for constructing and testing matrix presentations of the representations of <span class="SimpleMath">\(\mathrm{SL}_2(\mathbb{Z})\)</span> whose kernels are congruence subgroups of <span class="SimpleMath">\(\mathrm{SL}_2(\mathbb{Z})\)</span>.</p>

<p>Irreducible representations of prime-power level are constructed individually by using the Weil representations of quadratic modules, and from these a list of all representations of a given degree or level can be produced. Each representation is represented by a pair <span class="SimpleMath">\((S,T)\)</span>, where <span class="SimpleMath">\(S\)</span> is a symmetric, unitary matrix and <span class="SimpleMath">\(T\)</span> is a diagonal matrix of finite order; this format is designed for the study of modular tensor categories in particular.</p>

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<h4>1.1 <span class="Heading">Installation</span></h4>

<p>To install <code class="code">SL2Reps</code>, first download it from <span class="URL"><a href="https://snw-0.github.io/sl2-reps/">https://snw-0.github.io/sl2-reps/</a></span>, then place it in the <code class="code">pkg</code> subdirectory of your GAP installation (or in the <code class="code">pkg</code> subdirectory of any other GAP root directory, for example one added with the <code class="code">-l</code> argument).</p>

<p><code class="code">SL2Reps</code> is then loaded with the GAP command</p>

<p><code class="code">gap> LoadPackage( "SL2Reps" );</code></p>

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<h4>1.2 <span class="Heading">Usage</span></h4>

<p>Specific irreducible representations may be constructed via the methods in Chapter <a href="chap3_mj.html#X7C4165447B8AB223"><span class="RefLink">3</span></a>, while lists of irreducible representations with a given degree or level may be constructed with those in Chapter <a href="chap4_mj.html#X8168FF017B2C0BB2"><span class="RefLink">4</span></a>.</p>

<p>This package uses an <code class="code">InfoClass</code>, <code class="code">InfoSL2Reps</code>. It may be set to <code class="code">0</code> (silent), <code class="code">1</code> (info), or <code class="code">2</code> (verbose). To change it, use</p>

<p><code class="code">gap> SetInfoLevel( InfoSL2Reps, k );</code></p>


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