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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1993-1102225-X

Keywords:
Hilbert modular form,
newform,
character twists

Article copyright:
© Copyright 1993
American Mathematical Society