In this paper we give an example of a noncongruence subgroup whose
three-dimensional space of cusp forms of weight 3 has the following properties.
For each of the four residue classes of odd primes modulo 8 there is a basis
whose Fourier coefficients at infinity satisfy a three-term Atkin and
Swinnerton-Dyer congruence relation, which is the p-adic analogue of the
three-term recursion satisfied by the coefficients of classical Hecke eigen
forms. We also show that there is an automorphic L-function over Q
whose local factors agree with those of the l-adic Scholl representations
attached to the space of noncongruence cusp forms.Comment: Last version, to appear on Math Annale