  We analyse the symmetries of a class of A-type little string theories that
are engineered by $N$ parallel M5-branes with M2-branes stretched between them.
This paper deals with the so-called reduced free energy, which only receives
contributions from the subset of the BPS states that carry the same charges
under all the Cartan generators of the underlying gauge algebra. We argue (and
check explicitly in a number of examples) that the former is invariant under
the paramodular group $\Sigma_N\subset Sp(4,\mathbb{Q})$, which gets extended
to a subgroup of $Sp(4,\mathbb{R})$ in the Nekrasov-Shatashvili-limit. This
extension agrees with the observation made in arXiv:1706.04425 that these BPS
states form a symmetric orbifold CFT. Furthermore, we argue that $\Sigma_N$
(along with other symmetries) places strong constraints on the BPS counting
function that governs the intersection between the M5- and M2-branes.
