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

Abstract

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.

arXiv commentTo appear in Archiv der Mathematik

References in corpus (2)

• On Shimura's decomposition
• Hecke operators in half-integral weight

Cited by in corpus (1)

• Newforms of half-integral weight: the minus space counterpart