How can I find all coset representatives for $\Gamma_0(2)$ in $SL_2(\mathbb{Z})$?

Question

$\Gamma_0(2)=\Big\lbrace\begin{pmatrix}a&b\\c&d\end{pmatrix} \in SL_2(\mathbb{Z}):c\equiv0 \ (mod \ 2) \Big\rbrace$

I know that |$SL_2(\mathbb{Z}):\Gamma_0(2)|=3 .$ Thererfore there are 3 cosets . Now for fixed $a\in SL_2(\mathbb{Z})$ I can consider the left coset $a\Gamma_0(2)$ . Now my problem is how to find all these cosets .