  We use the description of the Picard modular surface for discriminant $-3$ as
a moduli space of curves of genus $3$ to generate all vector-valued Picard
modular forms from bi-covariants for the action of ${GL}_2$ on the space of
pairs of binary forms of bidegree $(4,1)$. The universal binary forms of degree
$4$ and $1$ correspond to a meromorphic modular form of weight $(4,-2)$ and a
holomorphic Eisenstein series of weight $(1,1)$.
