Twists of Hilbert modular forms

Shemanske, Thomas R.; Walling, Lynne H.

doi:10.1090/S0002-9947-1993-1102225-X

Twists of Hilbert modular forms
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by Thomas R. Shemanske and Lynne H. Walling PDF

Trans. Amer. Math. Soc. 338 (1993), 375-403 Request permission

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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