  We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert
manifold with 4-singular fibers. We define the Eichler integrals of the modular
forms with half-integral weight, and we show that the invariant is rewritten as
a sum of the Eichler integrals. Using a nearly modular property of the Eichler
integral, we give an exact asymptotic expansion of the WRT invariant in
$N\to\infty$. We reveal that the number of dominating terms, which is the
number of the non-vanishing Eichler integrals in a limit $\tau\to
N\in\mathbb{Z}$, is related to that of lattice points inside 4-dimensional
simplex, and we discuss a relationship with the irreducible representations of
the fundamental group.
