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On twisting operators and newforms of half-integral weight II – Complete theory of newforms for Kohnen space
- Source :
- Nagoya Mathematical Journal. 149:117-171
- Publication Year :
- 1998
- Publisher :
- Cambridge University Press (CUP), 1998.
-
Abstract
- The author continues his previous work with the purpose of establishing a theory of newforms in the case of half-integral weight. In this paper, the author formulates and proves a complete theory of newforms for Kohnen space. Kohnen space is an important canonical subspace in the space of cusp forms of half-integral weight k + 1/2 (k > 0). Every Hecke common eigenform in Kohnen space corresponds to a primitive form of integral weight 2k and of odd level via Shimura Correspondence.These newforms for Kohnen space satisfy the Strong multiplicity One theorem. Moreover, we explicitly determine the corresponding primitive form (of weight 2k) to each newform for Kohnen space. The space of oldforms is also explicitly described.In order to find all newforms for Kohnen space, the author needs a certain non-vanishing property of Fourier coefficients of cusp forms. Such property proves by using representation theory of finite linear groups. The method of proof of newform theory is mainly based on trace formulae and trace relations.
- Subjects :
- Cusp (singularity)
Discrete mathematics
Pure mathematics
Trace (linear algebra)
010308 nuclear & particles physics
General Mathematics
010102 general mathematics
Space (mathematics)
01 natural sciences
Representation theory
0103 physical sciences
Order (group theory)
Eigenform
Complete theory
0101 mathematics
Shimura correspondence
Mathematics
Subjects
Details
- ISSN :
- 21526842 and 00277630
- Volume :
- 149
- Database :
- OpenAIRE
- Journal :
- Nagoya Mathematical Journal
- Accession number :
- edsair.doi...........c913729bd0103dfd932342ed7e59d2e2