I will present a proof of the following conjecture of Baker–Reid: given any rational homology 3-sphere N, there are at most finitely many congruence arithmetic quotients of hyperbolic space which are homeomorphic to the complement of a link in N. There are many ingredients to the proof but the final step is an asymptotic lower bound on the cuspidal homology of certain congruence subgroups of Bianchi groups. I will therefore use the conjecture as an excuse to talk about various ways to give such bounds, and finally present the somewhat new method we used to get to the result we needed. (Joint work with Steffen Kionke).