We represent the $105$ automorphic forms on the $5$-dimensional complex ball $\mathbb B^5$ constructed by Matsumoto-Terasoma as the products of four linear combinations of the pull backs of theta constants under an embedding of $\mathbb B^5$ into the Siegel upper half space of degree $6$. They were used to describe the inverse of the period map for the family of the $4$-fold coverings of the complex projective line branching at eight points.
"Automorphic forms on the $5$-dimensional complex ball with respect to the Picard modular group over $\mathbb Z[i]$." Hokkaido Math. J. 36 (1) 143 - 173, February 2007. https://doi.org/10.14492/hokmj/1285766656