  In this paper we study the compatible family of degree-4 Scholl
representations $\rho_{\ell}$ associated with a space $S$ of weight $\kappa> 2$
noncongruence cusp forms satisfying Quaternion Multiplications over a
biquadratic field $K$. It is shown that when either $K$ is totally real or
$\kappa$ is odd, $\rho_\ell$ is automorphic, that is, its associated L-function
has the same Euler factors as the L-function of an automorphic form for
$GL_4(\mathbb Q)$. Further, it yields a relation between the Fourier
coefficients of noncongruence cusp forms in $S$ and those of certain
automorphic forms via the three-term Atkin and Swinnerton-Dyer congruences.
