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HECKE OPERATORS AND DRINFELD CUSP FORMS OF LEVEL $\boldsymbol {t}$

Part of: Discontinuous groups and automorphic forms Special matrices

Published online by Cambridge University Press:  15 June 2022

ANDREA BANDINI Open the ORCID record for ANDREA BANDINI [Opens in a new window]  and
MARIA VALENTINO Open the ORCID record for MARIA VALENTINO [Opens in a new window]
ANDREA BANDINI*
Affiliation:
Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, Pisa 56127, Italy
MARIA VALENTINO
Affiliation:
Dipartimento di Matematica e Informatica, Università della Calabria, Ponte P. Bucci, Cubo 30B, Rende 87036 (CS), Italy e-mail: maria.valentino@unical.it
*
e-mail: andrea.bandini@unipi.it
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Abstract

We use a linear algebra interpretation of the action of Hecke operators on Drinfeld cusp forms to prove that when the dimension of the $\mathbb {C}_\infty $-vector space $S_{k,m}(\mathrm {{GL}}_2(\mathbb {F}_q[t]))$ is one, the Hecke operator $\mathbf {T}_t$ is injective on $S_{k,m}(\mathrm {{GL}}_2(\mathbb {F}_q[t]))$ and $S_{k,m}(\Gamma _0(t))$ is a direct sum of oldforms and newforms.

Keywords

Drinfeld cusp formHecke operatorAtkin–Lehner operatornewformoldform

MSC classification

Primary: 11F52: Modular forms associated to Drinfel'd modules
Secondary: 11F25: Hecke-Petersson operators, differential operators (one variable) 15B99: None of the above, but in this section

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 107 , Issue 2 , April 2023 , pp. 184 - 195
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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References

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