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Transactions of the American Mathematical Society

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On lifting Hecke eigenforms


Author: Lynne H. Walling
Journal: Trans. Amer. Math. Soc. 328 (1991), 881-896
MSC: Primary 11F41; Secondary 11F27, 11F60
DOI: https://doi.org/10.1090/S0002-9947-1991-1061779-0
MathSciNet review: 1061779
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Abstract: A classical Hilbert modular form $ f \in {\mathcal{M}_k}({\Gamma _0}(\mathcal{N},\mathcal{I}),{\chi _\mathcal{N}})$ cannot be an eigenform for the full Hecke algebra. We develop a means of lifting a classical form to a modular form $ F \in { \oplus _\lambda }{\mathcal{M}_k}({\Gamma _0}(\mathcal{N},{\mathcal{I}_\lambda }),{\chi _\mathcal{N}})$ which is an eigenform for the full Hecke algebra. Using this lift, we develop the newform theory for a space of cusp forms $ {\mathcal{S}_k}({\Gamma _0}(\mathcal{N},\mathcal{I}),{\chi _\mathcal{N}})$; we also use theta series to construct eigenforms for the full Hecke algebra.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1991-1061779-0
Keywords: Hilbert modular forms, newforms, theta series, quadratic forms
Article copyright: © Copyright 1991 American Mathematical Society

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