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][1] studied by Zagier and Cooper.

**P.S.2:** A similar table can be created relating level $2$ with level $8$.

  [1]: https://www.researchgate.net/publication/257642843_Sporadic_sequences_modular_forms_and_new_series_for_1p