On Atkin-Swinnerton-Dyer congruence relations

In this paper we exhibit a noncongruence subgroup $\text{G}$ whose space of weight 3 cusp forms $S_3(\text{G})$ admits a basis satisfying the Atkin-Swinnerton-Dyer congruence relations with two weight 3 newforms for certain congruence subgroups. This gives a modularity interpretation of the motive attached to $S_3(\text{G})$ by A. Scholl and also verifies the Atkin-Swinnerton-Dyer congruence conjecture for this space.