Mathematics of Computation

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

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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