The cusp amplitudes and quasi-level of a congruence subgroup of SL2 over any Dedekind domain

We extend some algebraic properties of the classical modular group SL2(ℤ) to equivalent groups in the theory of Drinfeld modules, in particular, properties which are important in the theory of modular curves. We study cusp amplitudes and the level of a (congruence) subgroup of SL2(D) for any Dedekind domain D, as ideals of D. In particular, we extend a remarkable result of Larcher. We introduce finer notions of quasi-amplitude and quasi-level which are not required to be ideals and encode more information about the subgroup. Our results also provide several new necessary conditions for a subgroup of SL2(D) to be a congruence subgroup.