  It is well known that Ramanujan conjectured congruences modulo powers of $5$,
$7$ and and $11$ for the partition function. These were subsequently proved by
Watson (1938) and Atkin (1967). In 2009 Choi, Kang, and Lovejoy proved
congruences modulo powers of $5$ for the crank parity function. The generating
function for the analogous rank parity function is $f(q)$, the first example of
a mock theta function that Ramanujan mentioned in his last letter to Hardy.
Recently we proved congruences modulo powers of $5$ for the rank parity
function, and here we extend these congruences for powers of $7$. We also show
how these congruences imply congruences modulo powers of $5$ and $7$ for the
coefficients of the related third order mock theta function $\omega(q)$, using
Atkin-Lehner involutions and transformation results of Zwegers. Finally we a
prove a family of congruences modulo powers of $7$ for the crank parity
function.
