Van der Geer's student Christiaan van Dorp could settle odd weight of $Sym^6$ for $Sp(2,\mathbb{Z})$ in his M.Sc. thesis

Christiaan van Dorp. Generators for a module of vector-valued Siegel modular forms of degree 2, http://arxiv.org/abs/1301.2910 .

The whole thesis can be found here. He gives a nice overview over the field and presents a shortened version of the original $Sym^2$ cases.

Van der Geer's student Christiaan van Dorp could settle odd weight of $Sym^6$ for $Sp(2,\mathbb{Z})$ in his 2011 M.Sc. thesis

Christiaan van Dorp. Generators for a module of vector-valued Siegel modular forms of degree 2, http://arxiv.org/abs/1301.2910 .

The whole thesis can be found here. He gives a nice overview over the field and presents a shortened version of the original $Sym^2$ cases.

Van der Geer's student Christiaan van Dorp could settle odd weight of $Sym^6$ for $Sp(2,\mathbb{Z})$ in his M.Sc. thesis

Christiaan van Dorp. Generators for a module of vector-valued Siegel modular forms of degree 2, http://arxiv.org/abs/1301.2910 .

Van der Geer's student Christiaan van Dorp could settle odd weight of $Sym^6$ for $Sp(2,\mathbb{Z})$ in his M.Sc. thesis

Christiaan van Dorp. Generators for a module of vector-valued Siegel modular forms of degree 2, http://arxiv.org/abs/1301.2910 .

The whole thesis can be found here. He gives a nice overview over the field and presents a shortened version of the original $Sym^2$ cases.