  We show that the normalized supercharacters of principal admissible modules
over the affine Lie superalgebra $\hat{s\ell}_{2|1}$ (resp.
$\hat{ps\ell}_{2|2}$) can be modified, using Zwegers' real analytic
corrections, to form a modular (resp. $S$-) invariant family of functions.
Applying the quantum Hamiltonian reduction, this leads to a new family of
positive energy modules over the N=2 (resp. N=4) superconformal algebras with
central charge $3(1-\frac{2m+2}{M})$, where $m \in \mathbb{Z}_{\geq 0}$, $M\in
\mathbb{Z}_{\geq 2}$, $\gcd(2m+2,M)=1$ if $m>0$ (resp. $6(\frac{m}{M}-1)$,
where $m \in \mathbb{Z}_{\geq 1}, M\in \mathbb{Z}_{\geq 2}$, $\gcd(2m,M)=1$ if
$m>1$), whose modified characters and supercharacters form a modular invariant
family.
