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The basis problem for modular forms on $\Gamma _0(N)$

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)
MathSciNet review: 960090
MSC: Primary 11F11

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Table of Contents


  • 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
American Mathematical Society