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<p>Given an irreducible representation of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1239_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{SL}_2(\mathbb {F}_q)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>SL</mtext> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="double-struck">F</mi> <mi>q</mi> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for an odd prime <i>q</i>, we find the dimension of the space of cusp forms with respect to the full modular group taking values in the representation space. The dimension equals the multiplicity of the representation in the space of classical cusp forms with respect to the principal congruence subgroup of level <i>q</i>.</p>

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On the dimensions of certain spaces of vector-valued cusp forms

  • 期刊论文

  • 发表日期：

    2025年11月5日

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  • Darshan Nasit

摘要

Given an irreducible representation of \(\textrm{SL}_2(\mathbb {F}_q)\) SL 2 ( F q ) for an odd prime q, we find the dimension of the space of cusp forms with respect to the full modular group taking values in the representation space. The dimension equals the multiplicity of the representation in the space of classical cusp forms with respect to the principal congruence subgroup of level q.