  We study $\ell$-regular partitions by defining a sequence of modular forms of
level $\ell$ and quadratic character which encode their $\ell$-adic behavior.
We show that this sequence is congruent modulo increasing powers of $\ell$ to
level $1$ modular forms of increasing weights. We then prove that certain
$\mathbb{Z}/\ell^m\mathbb{Z}$-modules generated by our sequence are isomorphic
to certain subspaces of level $1$ cusp forms of weight independent of the power
of $\ell$, leading to a uniform bound on the ranks of those modules and
consequently to $\ell$-adic relations between $\ell$-regular partition values.
