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 F_{p} and are labelled by their U_{p}-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.
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 |