paper

Determination of Hilbert modular forms using squarefree coefficients

arXiv:2403.16012 · doi:10.1016/j.jnt.2026.07.011

Abstract

Let (over ) be a totally real number field of narrow class number . We generalize a result of Kohnen on the determination of half integral weight modular forms by their Fourier coefficients supported on squarefree (algebraic) integers. We also give a soft proof that infinitely many Fourier coefficients supported on squarefree integers are non-vanishing.

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Determination of Hilbert modular forms using squarefree coefficients · wovepaper