Level and index in the modular group
Wilson Stothers · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1984
Synopsis It is shown that the index of a congruence subgroup of the modular group cannot be less than the level of the subgroup. This allows a number of existence theorems about non-congruence subgroups. The level of a subgroup of the modular group can be defined in terms of the action on Q ∪ {∞}. We define a similar action to get information on congruence subgroups. In fact, we get a more powerful result, but this appears to be the most useful version.