The coefficients of the generating function (q; q) α ∞ produce pα(n) for α ∈ Q. In particular, when α = ?1, the partition function is obtained. Recently, Chan and Wang studied congruences for pα(n) and gave several infinite families of congruences of the form pα(`n + c) ≡ 0 (mod `) for primes ` and integers c. Expanding upon their work, given adequate α, we use the lacunarity of the powers of the Dedekind-eta function to raise the modulus of Chan and Wang’s congruences to higher powers of `. In addition, we generate new infinite classes of congruences through the multiplicative properties of the coefficients of Hecke eigenforms. This allows us to prove new families of congruences such as: p? 1 8 (72n + 5) ≡ 0 (mod 72 ).
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