@b4c50e1b Excuse me, thank you for the nice explanation! I have a question, is there any group larger than the SL(2, Z) which still has some nice properties, e.g. notion of modular forms? I wonder how we can distinguish the black and yellow regions in your figure, since they are combined into the fundamental region of SL(2, Z). If we consider some congruence subgroups, the ability to distinguish becomes weaker, but I don't know if we can consider the group containing contains SL(2, Z) and distinguish the yellow and black regions. Thank you!