  In this paper we show that Atkin and Swinnerton-Dyer type of congruences hold
for weakly modular forms (modular forms that are permitted to have poles at
cusps). Unlike the case of original congruences for cusp forms, these
congruences are nontrivial even for congruence subgroups. On the way we provide
an explicit interpretation of the de Rham cohomology groups associated to
modular forms in terms of "differentials of the second kind". As an example, we
consider the space of cusp forms of weight 3 on a certain genus zero quotient
of Fermat curve X^N+Y^N=Z^N. We show that the Galois representation associated
to this space is Grossencharacter of a cyclotomic field $\Q(\zeta_N)$.
Moreover, for N=5 the space does not admit a "$p$-adic Hecke eigenbasis" for
(non-ordinary) primes $p\equiv 2,3 \pmod{5}$, which provides a counterexample
for original Atkin and Swinnerton-Dyer speculaction (see [2], [7], [8]).
