Critical values, congruences, Selmer groups

Since the seminar I am moderating is called congruences, I'll start off by explaining the possibilities for the composition factors of the reduction mod p of the type of 4-dimensional Galois representation coming from a CY 3-fold, and comparing these with the kinds of congruences observed by Anton Mellit, calling on him to report on observations about pairs of congruences and common values of $p$. This would set the scene. At some point later I could say something about how for at least one of the three kinds of such congruences, it should lead to an element of order $p$ in some Selmer group, how that appears in the Bloch-Kato conjecture, which then predicts the appearance of $p$ in an $L$-value, comparing and contrasting with the cases of congruences for Saito-Kurokawa lifts, and congruences connected with $p$-torsion on elliptic curves.