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

TL;DR

This paper explicitly describes generators for the graded ring of modular forms on the Cayley half-space of degree two, showing it can be generated by Eisenstein series and providing constructions for a specific skew-symmetric form.

Contribution

It provides explicit generators for the graded ring of modular forms on the Cayley half-space, building on previous work by determining concrete forms and their constructions.

Findings

The graded ring is generated by Eisenstein series.

Dimensions of homogeneous components are calculated.

Two constructions for the skew-symmetric form of weight 252 are provided.

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.