Constructing vector-valued Siegel modular forms from scalar-valued Siegel modular forms

TL;DR

This paper introduces an efficient method to construct vector-valued Siegel modular forms from scalar-valued forms, revealing strong relations between forms of different genera and producing key cusp forms like Delta.

Contribution

It provides a simple, efficient construction method for vector-valued Siegel modular forms from scalar-valued forms, highlighting their interrelations across genera.

Findings

Constructs vector-valued forms from scalar-valued forms.

Produces the smallest weight cusp forms like Delta.

Demonstrates strong relations between modular forms of different genera.

Abstract

This paper gives a simple method for constructing vector-valued Siegel modular forms from scalar-valued ones. The method is efficient in producing the siblings of Delta, the smallest weight cusp forms that appear in low degrees. It also shows the strong relations between these modular forms of different genera. We illustrate this by a number of examples.