  We study the BPS spectrum of Little String Theory for bound states of
M5-branes wrapped on six manifold of product topology $M_4\times\Sigma_2$ and
the apparence of multi-loop $\theta$-functions in a supersymmetric index
calculation. We find a total reconstruction of the g-loop heterotic
contribution in the case of a double K3 M-theory compactification. Moreover, we
consider total wrapping of M5-branes on del Pezzo surfaces $B_k$ and, by
studying the relevant amplitude, we notice the arising of $\theta$-functions
relative to BPS strings on $T^{k-1}$, i.e. membranes on $T^k$. This happens
because of beautiful relations between four dimensional SYM theories and CFTs
in two dimensions and seems to be linked to a duality recently observed by
A.Iqbal, A.Neitzke and C.Vafa in.
