Structure theorems for vector valued Siegel modular forms of degree 2 and weight detk ⊗Sym(10)

Abstract

We prove the explicit structure theorems of modules [Formula: see text] of vector valued Siegel modular forms of degree [Formula: see text], where [Formula: see text] runs over the set of even integers or odd integers. We also check the conjecture given by Ibukiyama [Vector valued Siegel modular forms of symmetric tensor weight of small degrees, Comment. Math. Univ. St. Pauli 61 (2012) 51–75.] for modules of vector valued Siegel modular forms of degree [Formula: see text] of weights [Formula: see text] and [Formula: see text].