  We calculate the Schur index of the ${\cal N}=4$ $U(N)$ SYM with finite $N$
via the AdS/CFT correspondence as the contribution of D3-branes wrapped on
contractible cycles in $\boldsymbol{S}^5$ on some assumptions motivated by
preliminary analyses. As far as we have checked numerically it agrees with the
index calculated on the gauge theory side. In a certain limit it reproduces the
analytic result given by Bourdier, Drukker, and Felix.
