On certain vector valued Siegel modular forms of degree two

Siegel Modular Forms and Their Applications

“…The direct sum ⊕ k M j,k (Γ 2 ) for fixed j is a module over the ring M cl = ⊕M 0,k (Γ 2 ) of classical Siegel modular forms and we know generators of this module for j = 2 and j = 4 and even j = 6 due to Satoh and Ibukiyama, cf. [85,47,48].…”

“…Using this operation (an instance of Cohen-Rankin operators) Satoh showed in [85] that ⊕ k≡0(2) M 2,k is generated over the ring ⊕ k M k (Γ 2 ) of classical Siegel modular forms by such [f, g] with f and g classical Siegel modular forms. We give a little table with dimensions for dim S j,k (Γ 2 ) for 4 ≤ k ≤ 20, 0 ≤ j ≤ 18 with j even: …”

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

“…In other words, M 0 Sym(10) (Γ (2) ) is generated by 13 modular forms of determinant weights 6,8,10,10,12,12,14,14,14,16,16,18,20 and they satisfy two fundamental relations. M 1 Sym(10) (Γ (2) ) is generated by 13 modular forms of determinant weights 9,11,13,15,15,15,17,17,17,19,19,21, 23 and they satisfy two fundamental relations.…”

“…(3) By structure theorems of M Sym(2) (Γ (2) ) (cf. [17], [7]) and the result on a Wronskian of scalar valued Siegel modular forms (cf. [ Thus we have f 2,0 = χ 35 and f 2,1 = χ 2 35 up to non-zero constants.…”

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

“…Thus we also have (Γ 2 ) and the fundamental relations among them have been examined by several authors. Satoh [11] proved the structure theorem for A Here Z = z11 z12 z12 z22 is the parameter of the Siegel upper half space H 2 of degree two and…”