The graded ring of modular forms on the Cayley half-space of degree two

Abstract

Hashimoto and Ueda determined the weights of generators of the graded ring of modular forms on the Cayley half-space of degree two. In this paper we describe explicit generators. We show that the graded ring can be generated by Eisenstein series by calculating the dimensions of the homogeneous components. Moreover we give two distinct constructions for the skew-symmetric form of weight 252.