## Determining Siegel modular forms of half-integral weight by their fundamental Fourier coefficients

### Volume 195 / 2020

Acta Arithmetica 195 (2020), 269-279
MSC: Primary 11F30, 11F46; Secondary 11F50.
DOI: 10.4064/aa190308-22-1
Published online: 27 May 2020

#### Abstract

We prove that a non-zero Siegel cusp form of half-integral weight and degree 2 on $\Gamma _0^{(2)}(4)$ has infinitely many non-zero Fourier coefficients indexed by semi-integral matrices having fundamental discriminant. This is the half-integral weight version of the result proved by A. Saha [Math. Ann. 355 (2013), 363–380] in the case of Siegel modular forms of integral weight and degree 2.