In 1973, Swinnerton-Dyer completely classified all congruences for coefficients of normalized eigenforms in weights k ∈ {12, 16, 18, 20, 22, 26} on Γ_0(1) = SL_2(Z) using the theory of modular Galois representations. In this talk, we classify congruences of the Type I and Type II considered by Swinnerton-Dyer for the coefficients of eta-quotient newforms in S_k(N, χ), k ≥ 1 and prove them using theory of filtrations modulo primes. Further, we prove extensions of these congruences modulo prime powers.

(Joint with Matthew Boylan, Eddie O’ Sullivan, Jin Xiaolan and Henry Stone)