in his landmark paper ``modular forms and the eisenstein ideal,'' mazur studied congruences modulo a prime p between the hecke eigenvalues of an eisenstein series and the hecke eigenvalues of cusp forms, assuming these modular forms have weight 2 and prime level n. he asked about generalizations to squarefree levels n. i will present some work on such generalizations, which is joint with preston wake and catherine hsu.