On the computation of the determinant of vector-valued Siegel modular forms

Abstract

Let A(Γ2) denote the ring of scalar valued Siegel modular forms of degree two, level 1 and even weights. In this paper, we prove the determinant of a basis of the module of vector valued Siegel modular forms ⊕ k≡ mod 2 Adetk ⊗Sym(j)(Γ2) over A (Γ2) is equal to a power of the cusp form of degree two and weight 35 up to a constant. Here j = 4, 6 and = 0, 1. The main result in this paper was conjectured by Ibukiyama [7].