Fundamental domains for congruence subgroups of SL2 in positive characteristic

In this work, we construct fundamental domains for congruence subgroups of SL2(Fq[t]) and PGL2(Fq[t]). Our method uses Gekeler's description of the fundamental domains on the Bruhat–Tits tree X=Xq+1 in terms of cosets of subgroups. We compute the fundamental domains for a number of congruence subgroups explicitly as graphs of groups using the computer algebra system Magma.