  New congruences are found for Andrews' smallest parts partition function
spt(n). The generating function for spt(n) is related to the holomorphic part
alpha(24z) of a certain weak Maass form M(z) of weight 3/2. We show that a
normalized form of the generating function for spt(n) is an eigenform modulo 72
for the Hecke operators T(p^2) for primes p > 3, and an eigenform modulo t for
t = 5, 7 or 13 provided that (t, 6p) = 1. The result for the modulus 3 was
observed earlier by the author and considered by Ono and Folsom. Similar
congruences for higher powers of t (namely 5^6, 7^4 and 13^2) occur for the
coefficients of the function alpha(z). Analogous results for the partition
function were found by Atkin in 1966. Our results depend on the recent result
of Ono that M[p](z/24) is a weakly holomorphic modular form of weight 3/2 for
the full modular group where
  M[p](z) = M(z)|T(p^2) - chi(p)(1 + p)M(z).

Number Theory