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We represent the 105 automorphic forms on the 5-dimensional complex ball B 5 constructed by Matsumoto-Terasoma as the products of four linear combinations of the pull backs of theta constants under an embedding of 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 $\mathbb Z[i]$