Reduction of positive definite binary quadratic forms over congruence subgroups

Question

Let $\Gamma_0(N)$ be a congruence subgroup of $\mathrm{SL}_2(\mathbb{Z})$ and $Q(x,y)$ be a positive definite binary quadratic form with leading coefficient $a$ divisible by $N$. Can someone give me a reference showing how to find the matrix in $\Gamma_0(N)$ that takes $Q$ to its reduced form for $\Gamma_0(N)$? I am familiar with the algorithm for $\mathrm{SL}_2(\mathbb{Z})$ but am having a hard time finding such a process in the literature for a general $\Gamma_0(N)$.