I was wondering if anyone could give me tips on the following question:

Suppose $\alpha \in\text{GL}_2^{+}(\mathbb{Q})$ has integral entries and is such that det$(\alpha) = D > 0$.

If $\Gamma$ is a congruence subgroup of level $N$ then $\alpha^{-1}\Gamma\alpha$ contains a congruence subgroup of level $ND$.

I am really just starting out with modular forms so don't know a great deal of stuff. I hope I haven't missed something simple.