On the concept of level for subgroups of SL2 over arithmetic rings

We define the concept of level for arbitrary subgroups Gamma of finite inde x in the special linear group SL2(As), where As is the ring of S-integers o f a global field k provided that k is an algebraic number field, or card (S ) greater than or equal to 2. It is shown that this concept agrees with the usual notion of 'Stufe' for congruence subgroups. In the case SL2(O), O th e ring of integers of an imaginary quadratic number field, this criterion f or deciding whether or not an arbitrary subgroup of finite index is a congr uence subgroup is used to determine the minimum of the indices of non-congr uence subgroups.