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 $Sym^6$.

ncr commented on the proof in this mathoverflow thread :

I wrote to Kiyuna and he tells me that there are 18 generators: 6 of them are theta series (presumably products of theta constants) and the remaining 12 are a kind of Rankin-Cohen construction. I don't know much more but he tells me there will be a preprint in the next couple of weeks.

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 $Sym^6$.

ncr commented on the proof in this mathoverflow thread :

I wrote to Kiyuna and he tells me that there are 18 generators: 6 of them are theta series (presumably products of theta constants) and the remaining 12 are a kind of Rankin-Cohen construction. I don't know much more but he tells me there will be a preprint in the next couple of weeks.

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.

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 $Sym^6$.

ncr commented on the proof in this mathoverflow thread :

I wrote to Kiyuna and he tells me that there are 18 generators: 6 of them are theta series (presumably products of theta constants) and the remaining 12 are a kind of Rankin-Cohen construction. I don't know much more but he tells me there will be a preprint in the next couple of weeks.