I'm looking for a formula which gives the dimension of $\mathcal{S}_k(\Gamma_0(N))$ the space of cusp forms of weight $k$ and level $N$. I found the following statement for $k\geq 4$ $$\dim \mathcal{S}_k(\Gamma_0(N))=\frac{k-1}{12}\nu(N)+\left(\left\lfloor \frac{k}{4}\right\rfloor-\frac{k-1}{4}\right)\nu_2 (N)+\left(\left\lfloor \frac{k}{3}\right\rfloor-\frac{k-1}{3}\right)\nu_3 (N)-\frac{1}{2}\nu_{\infty}(N)$$ but I don't even know what $\nu(N)$, $\nu_2(N)$, $\nu_3(N)$ and $\nu_{\infty}(N)$ are...
Thanks a lot !