  We produce first examples of p-local height three TAF homology theories. The
corresponding one-dimensional formal groups arise as split summands of the
formal groups of certain abelian three-folds, the Shimura variety of which can
be reinterpreted as moduli of a family of Picard curves. This allows an
explicit description of an automorphic form valued genus in terms of the
coefficients of these curves. Moreover, our construction is such that the
theories naturally come with restriction maps to TAF theories of lower height.
