  In the paper "The universal Kummer threefold", Q. Ren, S. Sam, G. Schrader,
and B. Sturmfels (arXiv:1208.1229), conjectured equations for the universal
Kummer variety in genus 3 case. Though, most of these equations are obtained
from the Fourier-Jacobi expansion of relations among theta constants in genus
4, the more prominent one, Coble's quartic was obtained differently. The aim of
the current paper is to show that Coble's quartic can be obtained as
Fourier-Jacobi expansion of a relation among theta-constants in genus 4. We get
also one more relation that could be in the ideal described in "The universal
Kummer threefold".
