Generating Picard modular forms by means of invariant theory Dedicated to Don Zagier on the occasion of his 70th birthday

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).