1 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet2 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet
We continue and complete our previous paper ``Lifts of projective congruence groups'' concerning the question of whether there exist noncongruence subgroups of that are projectively equivalent to one of the groups or . A complete answer to this question is obtained: In case of such noncongruence subgroups exist precisely if and we additionally have either that or that is divisible by an odd prime congruent to modulo . In case of these noncongruence subgroups exist precisely if . As in our previous paper the main motivation for this question is the fact that the above noncongruence subgroups represent a fairly accessible and explicitly constructible reservoir of examples of noncongruence subgroups of that can serve as the basis for experimentation with modular forms on noncongruence subgroups.
American Mathematical Society. Proceedings, 2014, Vol 142, Issue 11, p. 3761-3770