There are three exceptional Galois groups $L_2(5)$, $L_2(7)$ and $L_2(11)$ . These are cited as one of Arnold's "trinities" and are connected with other trinities and the McKay Correspondence.

Ramanujan studied partition numbers and found congruence relations modulo powers of 5, 7 and 11. the recent dramatic breakthrough by Ken Ono throws some light on the reasons behind these congruences.

My question is whether there is any known connection between these two instances of the three primes 5, 7 and 11 appearing in these two places. I realise that these are just small numbers so it is not a great coincidence, but partitions are connected to other areas of mathematics so I wondered if some correspondence was known.