Rational eigenvectors in spaces of ternary forms
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Abstract:
We describe the explicit computation of linear combinations of ternary quadratic forms which are eigenvectors, with rational eigenvalues, under all Hecke operators. We use this process to construct, for each elliptic curve $E$ of rank zero and conductor $N < 2000$ for which $N$ or $N/4$ is squarefree, a weight 3/2 cusp form which is (potentially) a preimage of the weight two newform $\phi _{E}$ under the Shimura correspondence.References
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Additional Information
- Larry Lehman
- Affiliation: Department of Mathematics, Mary Washington College, Fredericksburg, Virginia 22401
- Email: llehman@mwc.edu
- Received by editor(s): January 17, 1995
- Received by editor(s) in revised form: February 7, 1996
- © Copyright 1997 American Mathematical Society
- Journal: Math. Comp. 66 (1997), 833-839
- MSC (1991): Primary 11E45; Secondary 11F37, 11G05
- DOI: https://doi.org/10.1090/S0025-5718-97-00821-1
- MathSciNet review: 1397445