Congruences between modular forms

These graphs show the congruences mod p between p-ordinary cusp forms of level Np. The vertices represent q-expansions of eigenforms in Fp and are labelled by their Up-eigenvalues (mod p). Vertices of the same colour are Galois conjugate and edges between vertices correspond to congruences. In particular, the loops indicate multiplicity, i.e. a vertex with m − 1 loops represents m Galois conjugate q-expansions that are all congruent mod p. Such multiplicity occurs when p ramifies in the Hecke eigenvalue field of the corresponding eigenform.

These graphs were generated by code we (of the "families of overconvergent modular symbols" project) wrote in Sage.
 p = 5, N = 23  p = 7, N = 37
Congruences of modular forms Congruences of modular forms