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ISSN 1088-6826(e) ISSN 0002-9939(p)

Level lowering for half-integral weight modular forms

Author(s): Jim Brown; Yingkun Li
Journal: Proc. Amer. Math. Soc. 138 (2010), 1171-1173.
MSC (2010): Primary 11F37, 11F80
Posted: December 9, 2009
MathSciNet review: 2578511
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Abstract: In this paper we provide a level lowering result for half-integral weight modular forms. The main ingredients are the Shimura map from half-integral weight modular forms to integral weight modular forms along with a level lowering result for integral weight modular forms due to Ribet. It is necessary to keep track of the parity of the weight as well as the character involved so that one can apply the Shintani lift to go back to a half-integral weight modular form and establish the result.

References:

1.: M. Manickham and B. Ramakrishnan, On Shimura, Shintani and Eichler-Zagier correspondences, Trans. Amer. Math. Soc. 352(6) (2000) 2601-2617. MR 1637086 (2000j:11061)
2.: K. Ribet, Report on mod $\ell$ representations of $\operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ , Motives (Seattle, WA, 1991), 639-676, Proc. Sympos. Pure. Math., 55(2), Amer. Math. Soc., Providence, RI, 1994. MR 1265566 (95d:11056)
3.: G. Shimura, On modular forms of half-integral weight, Ann. Math. 97 (1973) 440-481. MR 0332663 (48:10989)

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Additional Information:

Jim Brown
Affiliation: Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634
Email: jimlb@clemson.edu

Yingkun Li
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Address at time of publication: Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, California 90095-1555
Email: yingkun@caltech.edu, yingkun@math.ucla.edu

DOI: 10.1090/S0002-9939-09-10242-3
PII: S 0002-9939(09)10242-3
Keywords: Half-integral weight modular forms
Received by editor(s): January 14, 2009
Posted: December 9, 2009
Additional Notes: The authors would like to thank the referee for suggestions on how to strengthen and streamline the original arguments.
The second author was supported by a Summer Undergraduate Research Fellowship at California Institute of Technology and the John and Maria Laffin Trust.
Communicated by: Wen-Ching Winnie Li
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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