Rational eigenvectors in spaces of ternary forms

Lehman, Larry

doi:10.1090/S0025-5718-97-00821-1

Rational eigenvectors in spaces of ternary forms
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Math. Comp. 66 (1997), 833-839 Request permission

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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