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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Twists of Hilbert modular forms


Authors: Thomas R. Shemanske and Lynne H. Walling
Journal: Trans. Amer. Math. Soc. 338 (1993), 375-403
MSC: Primary 11F41
MathSciNet review: 1102225
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Abstract: The theory of newforms for Hilbert modular forms is summarized including a statement of a strong multiplicity-one theorem and a characterization of newforms as eigenfunctions for a certain involution whose Dirichlet series has a prescribed Euler product. The general question of twisting Hilbert modular newforms by arbitrary Hecke characters is considered and the exact level of a character twist of a Hilbert modular form is determined. Conditions under which the twist of a newform is a newform are given. Applications include a strengthening in the elliptic modular case of a theorem of Atkin and Li's regarding the characterization of imprimitive newforms as well as its generalization to the Hilbert modular case, and a decomposition theorem for certain spaces of newforms as the direct sum of twists of spaces of newforms of lower level.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1102225-X
PII: S 0002-9947(1993)1102225-X
Keywords: Hilbert modular form, newform, character twists
Article copyright: © Copyright 1993 American Mathematical Society