Totally non-congruence Veech groups

Veech groups are discrete subgroups of $\mathrm{SL}(2,\mathbb{R})$ which play an important role in the theory translation surfaces. For a special class surfaces called origamis or square-tiled surfaces, their finite index $\mathrm{SL}(2,\mathbb{Z})$. We show that each stratum space contains infinitely many whose group is totally non-congruence group, i.e., it surjects to $\mathrm{SL} (2,\mathbb{Z}/n\mathbb{Z})$ for any $n$.