Congruence subgroup action notation

Question

I noticed this notation in a mathematical paper and it wasn't defined, so I assume it must be standard. Let $\Gamma_0(N)$ be the congruence subgroup $$\left\{\pmatrix{a & b \\ c & d} : ad - bc = 1, c \equiv 0 \pmod N\right\}$$ of the modular group $\Gamma = \textrm{SL}_2(\mathbb{Z})$. The notation I encountered was $$\Gamma_{\infty} \backslash \Gamma_0(N).$$ My understanding is that this type of notation usually refers to the set of equivalence classes obtained from action of the group to the left of the slash on the set to the right of the slash, i.e. $\textrm{SL}_2(\mathbb{Z}) \backslash \mathbb{H}$. However, I'm not sure what $\Gamma_{\infty}$ is supposed to mean.