Representations of $G=\mathrm{SL}_2(\mathbb{Z}/4\mathbb{Z})$ on SAGE/GAP

Question

Let $G=\mathrm{SL}_2(\mathbb{Z}/4\mathbb{Z})$. I want to use SAGE/GAP to write a code that prints image of all irreducible representations of $G$, when applied on the matrix $\begin{pmatrix} 1 & 1\\ 0 & 1 \end{pmatrix}$. Is there a SAGE/GAP command available for doing this? I know the command for getting character table on both SAGE or GAP, but I am not really able to find the command for what I need.