a conjecture of serre (now a theorem of gross, edixhoven, and coleman-voloch) classifies pairs of weights where one finds modular forms congruent modulo a prime p in terms of local behavior at p. we discuss a generalization of this conjecture in higher rank. a key step in our work is the study of a certain subscheme of gaitsgory's $a^1$ affine grassmannian which shares properties with some affine springer fibers. this is joint work with b. le hung, b. levin, and s. morra.