  We use a dispersion representation based on unitarity and analyticity to
study the low energy $\gamma^* N\rightarrow \pi N$ process in the $S_{11}$
channel. Final state interactions among the $\pi N$ system are critical to this
analysis. The left-hand part of the partial wave amplitude is imported from
$\mathcal{O}(p^2)$ chiral perturbation theory result. On the right hand part,
the final state interaction is calculated through Omn\`es formula in $S$-wave.
It is found that good numerical fit can be achieved with only one subtraction
parameter, and the eletroproduction experimental data of multipole amplitudes
$E_{0+},\ S_{0+}$ in the energy region below $\Delta(1232)$ are well described
when the photon virtuality $Q^2 \leq 0.1 \mathrm{GeV}^2$. The $\gamma^* N$
coupling of the possible sub-threshold resonance in $S_{11}$ channel is also
investigated.
