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The basis problem for modular forms on $Γ_{0}(N)$

About this Title

Hiroaki Hijikata, Arnold K. Pizer and Thomas R. Shemanske

Publication: Memoirs of the American Mathematical Society
Publication Year: 1989; Volume 82, Number 418
ISBNs: 978-0-8218-2481-8 (print); 978-1-4704-0841-1 (online)
DOI: https://doi.org/10.1090/memo/0418
MathSciNet review: 960090
MSC: Primary 11F11

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Table of Contents

Chapters

• Introduction
• 1. Preliminaries
• 2. The trace formula for Hecke operators
• 3. Twisting newforms
• 4. Theta series
• 5. A representation-theoretic definition of Brandt matrices
• 6. Trace identities
• 7. Cuspidal theta series and newforms
• 8. The basis problem
• 9. Connections with representation theory
• 10. Examples