  In a recent work, we found formulas for the Fourier coefficients of
automorphic forms of type $G_2$: holomorphic Siegel modular forms on
$\mathrm{Sp}_6$ that are theta lifts from $G_2^c$, and cuspidal quaternionic
modular forms on split $G_2$. We have implemented these formulas in the
mathematical software SAGE. In this paper, we explain the formulas of our
recent paper and the SAGE implementation. We also deduce some theoretical
consequences of our SAGE computations.
