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Mathematics of Computation

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Rational eigenvectors in spaces of ternary forms

Author: Larry Lehman
Journal: Math. Comp. 66 (1997), 833-839
MSC (1991): Primary 11E45; Secondary 11F37, 11G05
MathSciNet review: 1397445
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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.

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Additional Information

Larry Lehman
Affiliation: Department of Mathematics, Mary Washington College, Fredericksburg, Virginia 22401

Keywords: Quadratic forms, modular forms, elliptic curves
Received by editor(s): January 17, 1995
Received by editor(s) in revised form: February 7, 1996
Article copyright: © Copyright 1997 American Mathematical Society