  We show that the ring of modular forms with characters for
$\mathrm{O}(2,4;\mathbb{Z})$ is generated by forms of weights 4, 4, 6, 8, 10,
10, 12, and 30 with three relations of weights 8, 20, and 60. The proof is
based on the study of a moduli space of K3 surfaces.
