  We report the first observation of the line shape of the $\Lambda(1405)$ from
electroproduction, and show that it is not a simple Breit-Wigner resonance.
Electroproduction of $K^+ \Lambda(1405)$ off the proton was studied by using
data from CLAS at Jefferson Lab in the range $1.0<Q^2<3.0$ (GeV/c)$^2$. The
analysis utilized the decay channels $\Sigma^+ \pi^-$ of the $\Lambda(1405)$
and $p \pi^0$ of the $\Sigma^+$. Neither the standard (PDG) resonance
parameters, nor free parameters fitting to a single Breit-Wigner resonance
represent the line shape. In our fits, the line shape corresponds approximately
to predictions of a two-pole meson-baryon picture of the $\Lambda(1405)$, with
a lower mass pole near 1368 MeV/c$^2$ and a higher mass pole near 1423
MeV/c$^2$. Furthermore, with increasing photon virtuality the mass distribution
shifts toward the higher mass pole.
