Let $\Gamma=\Gamma_o(N)$ be the congruence subgroup. Let $f\in C^\infty(\Gamma\backslash GL(2,R)/SO(2,R)R^*)$ be a Maass form. How shall we define its dual(contragredient) Maass form $f'$?

If $\Gamma=SL(2,Z)$, it is known that the dual Maass form should be $f'(z)=f(\omega (z^t)^{-1}\omega^{-1})$, where $$\omega=\begin{pmatrix}0&-1\\\ 1&0\end{pmatrix}.$$