Subspaces spanned by eigenforms with nonvanishing twisted central $L$-values

Published 29 Jun 2024 in math.NT | (2407.00532v1)

Abstract: In this paper, we construct explicit spanning sets for two spaces. One is the subspace generated by integral-weight Hecke eigenforms with nonvanishing quadratic twisted central $L$-values. The other is a subspace generated by half-integral weight Hecke eigenforms with certain nonvanishing Fourier coefficients. Along the way, we show that these subspaces are isomorphic via the Shimura lift.

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