Class polynomial obstructions to canonical congruences for the smallest parts function

We resolve an open conjecture by proving that the only "canonical'' Ramanujan congruence primes for the Andrews' smallest parts function, $\operatorname{spt}(n)$, are $\ell= 5, 7, 13$. Building on work of Ahlgren and Kim, we show that any such congruence forces square-index coefficients of certain w