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Ok let's start with Satoh's result which is the oldest one. It is on the full modular group $Sp(2,\mathbb{Z})$ and $Sym^2$ with even weight, i.e. $det^{2k}\otimes Sym^{2}$ Takakazu Satoh. On cer …

Ibukiyama proved the following results around the year 2000. They are also on the full modular group $Sp(2,\mathbb{Z})$. He covers odd weight of $Sym^2$, even weight of $Sym^6$, and all of $Sym^4$ …

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 m …

Ibukiyama's student Tomoya Kiyuna proved $Sym^8$ for $Sp(n,\mathbb{Z})$ in his Master's thesis. Here I haven't got any link or reference. AFAIK he uses similar techniques as Ibukiyama for $Sym^4$ and …

Aoki was the first one to tackle successfully a different group. In particular he solved the problem for $Sym^2$ and 3 groups ( and reproved it for $Sp(2,\mathbb{Z})$ ): $ \Gamma_{2,0}[2]:=\left\{ M …

I just wanted to share a tiny part of the solution with you. The group $\Gamma_{2,0}[2]$ is generated by the matrices $\begin{pmatrix}I_g & S \\ 0_g & I_g \end{pmatrix}$ where $S=S^t$, $\begin{pmatri …

What are modular forms or cusps forms, resp. ? We start with defining their common domains $\mathbb{H}_g$ as the set of symmetric $g \times g$ matrices with positive definite imaginary parts. The sym …

We should start with the definition of the symplectic group for an arbitrary ring $R$. The symplectic group $Sp(g,R)$ is the subgroup of $SL(2g,R)$ such that all elements satisfy $M=J_g^t M J_g$ with …

What are Siegel modular forms? We start with defining their common domains $\mathbb{H}_g$ as the set of symmetric $g \times g$ matrices with positive definite imaginary parts. The symplectic group $S …