The toal dimension of certain Sn modules determined by LLT polynomials associated with a Dyck path. Given a Dyck path, there is an associated (directed) unit interval graph $\Gamma$. Consider the expansion $$G_\Gamma(x;q) = \sum_{\kappa: V(G) \to \mathbb{N}_+} x_\kappa q^{\mathrm{asc}(\kappa)}$$ using the notation by Alexandersson and Panova. The function $G_\Gamma(x;q)$ is a so called unicellular LLT polynomial, and a symmetric function. Consider the Schur expansion $$G_\Gamma(x;q+1) = \sum_{\lambda} c^\Gamma_\lambda(q) s_\lambda(x).$$ By a result by Haiman and Grojnowski, all $c^\Gamma_\lambda(q)$ have non-negative integer coefficients. Thus, $G_\Gamma(x;q+1)$ is the Frobenius image of some (graded) $S_n$-module. The total dimension of this $S_n$-module is $$D_\Gamma = \sum_{\lambda} c^\Gamma_\lambda(1)f^\lambda$$ where $f^\lambda$ is the number of standard Young tableaux of shape $\lambda$. This statistic is $D_\Gamma$.