Let $f\in S_k(\Gamma_0(N))$ be a cusp form for $N>1$. Consider the following operators acting on $f$ via the natural action of $GL_2^{+}(\mathbb{R})$ : $$ W_N=\begin{pmatrix} 0 & -1\\ N & 0 \end{pmatrix}$$ $$ U_q=\sum\limits_{i=0}^{q-1}\begin{pmatrix} q & i\\ 0 & q \end{pmatrix}$$ for prime $q\mid N$. Does $U_qW_Nf=W_NU_qf$? Remark : The action for $\gamma=\begin{pmatrix} a & b\\ c & d\end{pmatrix}\in GL_2^{+}(\mathbb{R})$ is given by : $$\gamma f(z)= (\operatorname{det}(\gamma))^{k/2}(cz+d)^{-k} f\left(\dfrac{az+b}{cz+d}\right)$$. Any help is deeply appreciated.