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

Given an irreducible representation of 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...

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Veröffentlicht in:The Ramanujan journal Jg. 68; H. 3; S. 89
1. Verfasser: Nasit, Darshan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.11.2025
Springer Nature B.V
Schlagworte:
Combinatorics
Cusps
Decomposition
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Representations
Subgroups
Vector-valued cusp forms
11F75
11F70
Dimension formula
Character table
ISSN:1382-4090, 1572-9303
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Abstract Given an irreducible representation of 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 .
AbstractList Given an irreducible representation of SL2(Fq) 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.
Given an irreducible representation of 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 .
ArticleNumber 89
Author Nasit, Darshan
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Cites_doi 10.1017/CBO9780511609572
10.1080/00029890.1975.11993765
10.1007/BFb0065297
10.4064/aa145-4-4
ContentType Journal Article
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The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
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Keywords Vector-valued cusp forms
11F75
11F70
Dimension formula
Character table
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References W Fulton (1239_CR4) 1991
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Snippet Given an irreducible representation of 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...
Given an irreducible representation of SL2(Fq) for an odd prime q, we find the dimension of the space of cusp forms with respect to the full modular group...
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StartPage 89
SubjectTerms Combinatorics
Cusps
Decomposition
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Representations
Subgroups
Subtitle On the dimensions of certain spaces of vector-valued cusp forms
Title On the dimensions of certain spaces of vector-valued cusp forms
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