On lifting Hecke eigenforms
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- by Lynne H. Walling PDF
- Trans. Amer. Math. Soc. 328 (1991), 881-896 Request permission
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.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- 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