Per S. Cooper's request, a table relating level $1$ with level $9$ can be provided. The general form apparently is,
$$\frac{1}{\pi}=\frac{12}{(C)^{3/2}}\sum_{k=0}^\infty\tbinom{2k}{k} \tbinom{3k}{k}\tbinom{6k}{3k} \frac{3A\,k+B}{(-C^3)^k}$$ and, $$\frac{1}{\pi}=\frac{12}{(C-4\color{blue}\alpha)^{3/2}}\sum_{k=0}^\infty\tbinom{2k}{k}\sum_{j=0}^k \color{blue}\alpha^{k-3j} \tbinom{k}{3j}\tbinom{2j}{j}\tbinom{3j}{j} \frac{A\,k+B+N\color{blue}\alpha/3}{(-C+4\color{blue}\alpha)^k}$$
for general real $\color{blue}\alpha$ and where,
$$\begin{array}{|c|c|c|c|c|} \hline d&A&B&C&N\\ \hline 11&154/9&5&32&4/3\\ 19&114&25&96&4\\ 43 &5418 &789 &960 &24\\ 67 &87234 &10177 &5280 &76\\ 163 &181713378 &13591409 &640320 &1448\\ \hline \end{array}$$
The variables $A,B,C$ are known to have closed-form expressions in terms of $d$. Presumably $N$ should have as well.
P.S.1: Note also the equivalent forms,
$$s_k(\color{blue}\alpha)=\sum_{j=0}^k \color{blue}\alpha^{k-3j} \tbinom{k}{3j}\tbinom{2j}{j}\tbinom{3j}{j}=\sum_{j=0}^k \color{blue}\alpha^{k-3j} \tbinom{k}{j}\tbinom{k-j}{j}\tbinom{k-2j}{j}$$
where the latter form is used in H. Chan and S. Cooper's paper "Rational analogues of Ramanujan's series for 1/π". The case $\alpha=-3$,
$$s_k(-3) = 1, -3, 9, -21, 9, 297, -2421$$
is one of the six sporadic sequences studied by Zagier and Cooper.
P.S.2: A similar table can be created relating level $2$ with level $8$.