A Note on the Fourier coefficients of half-integral weight modular forms

Narasimha Kumar, Soma Purkait

Published 2013-04-24, updated 2014-03-10Version 3

In this note, we show that the algebraicity of the Fourier coefficients of half-integral weight modular forms can be determined by checking the algebraicity of the first few of them. We also give a necessary and sufficient condition for a half-integral weight modular form to be in Kohnen's +-subspace by considering only finitely many terms.