Define the groups
$$\Gamma_0^0(N,M) = \left.\left\{ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \in SL_2(\mathbb{Z}) \;\right|\; b = 0 \bmod N, \; c = 0 \bmod M. \right\}$$ and $$\Gamma_0(NM) = \left.\left\{ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \in SL_2(\mathbb{Z}) \;\right|\; c = 0 \bmod MN \right\}.$$
Are these subgroups conjugate in $SL_2(\mathbb{Z})$ and by which element?