Covolume of $PSL(2,\mathbb{Z})$ in $PSL(2,\mathbb{Q}_p)$

Question

Ihara proved that every torsion-free discrete subgroup in $SL(2,\mathbb{Q}_p)$ is free and of finite covolume. $SL(2,\mathbb{Z})$ is not torsion-free. Is it a discrete subgroup and what is the covolume ? (Assume the measure is normalized so that the subgroup of integral points is of measure 1)