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<p>In this paper, we construct Hecke eigenforms for two families of quotient spaces of meromorphic cusp forms on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\operatorname {SL}_2(\mathbb {Z})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mo>SL</mo> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">Z</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. We show that each quotient space in the first (resp. second family) is isomorphic as a Hecke module to the space <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(S_{2k}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mrow> <mn>2</mn> <mi>k</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> (resp. <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(M_{2k}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>M</mi> <mrow> <mn>2</mn> <mi>k</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>) of cusp forms (resp. holomorphic modular forms) of the same weight on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\operatorname {SL}_2(\mathbb {Z})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mo>SL</mo> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">Z</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Hecke eigenforms for meromorphic cusp forms

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月10日

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  • Kathrin Bringmann,
  • Ben Kane,
  • Michael H. Mertens

摘要

In this paper, we construct Hecke eigenforms for two families of quotient spaces of meromorphic cusp forms on \(\operatorname {SL}_2(\mathbb {Z})\) SL 2 ( Z ) . We show that each quotient space in the first (resp. second family) is isomorphic as a Hecke module to the space \(S_{2k}\) S 2 k (resp. \(M_{2k}\) M 2 k ) of cusp forms (resp. holomorphic modular forms) of the same weight on \(\operatorname {SL}_2(\mathbb {Z})\) SL 2 ( Z ) .