Solution (source code)

= Solution

Ignoring <spin> and working in the fixed <quarkonium> internal sector, the orbital degeneracy is $\sum_{l=0}^{n-1}(2l+1)=n^2$. Hence
$$
\boxed{g_1=1\quad(1s),\qquad g_2=4\quad(2s\text{ and three }2p\text{ states}).}
$$
No extra <spin> or colour multiplicity is being counted. The degeneracy between different $l$ at fixed $n$ is special to the <Coulomb potential>.