Journal article
Computations of vector-valued Siegel modular forms
Journal of number theory, v 133(11), pp 3921-3940
01 Nov 2013
Abstract
We carry out some computations of vector-valued Siegel modular forms of degree two, weight (k, 2) and level one, and highlight three experimental results: (1) we identify a rational eigenform in a three-dimensional space of cusp forms; (2) we observe that non-cuspidal eigenforms of level one are not always rational; (3) we verify a number of cases of conjectures about congruences between classical modular forms and Siegel modular forms. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an explicit description of the Hecke action on Fourier expansions. (C) 2013 Elsevier Inc. All rights reserved.
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Details
- Title
- Computations of vector-valued Siegel modular forms
- Creators
- Alexandru Ghitza - The University of MelbourneNathan C. Ryan - Bucknell UniversityDavia W Sulon - Drexel University, Mathematics
- Publication Details
- Journal of number theory, v 133(11), pp 3921-3940
- Publisher
- Elsevier
- Number of pages
- 20
- Grant note
- Australian Research Council Early Career Researcher Grant from the University of Melbourne
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000323295200020
- Scopus ID
- 2-s2.0-84880823520
- Other Identifier
- 991022064230604721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics