  Context. The repeating FRB121102 is so far the only extra-galactic Fast Radio
Burst found to be associated with a counterpart, a steady radio source with a
nearly flat spectral energy distribution (SED) in centimeter wavelengths.
  Aims. Previous observations of the persistent source down to $1.6$~GHz has
shown no sign of a spectral turn-over. Absorption is expected to eventually
cause a turn-over at lower frequencies. Better constraints on the physical
parameters of the emitting medium can be derived by detecting the
self-absorption frequency.
  Methods. We used the Giant Metre-Wave Radio Telescope (GMRT) during the
period of July to December 2017 to observe the source at low radio frequencies
down to $400$~MHz.
  Results. The spectral energy distribution of the source remains optically
thin even at $400$~MHz, with a spectral index of $\nu^{-(0.07 \pm 0.03)}$
similar to what is seen in Galactic plerions. Using a generic synchrotron
radiation model, we obtain constraints on properties of the non-thermal plasma
and the central engine powering it.
  Conclusions. We present low-frequency detections of the persistent source
associated with FRB121102. Its characteristic flat SED extends down to
$400$~MHz. Like Galactic plerions, the energy in the persistent source is
carried predominantly by leptons. The emitting plasma has a $B< 0.01$~G, and
its age is $> 524 \left(\frac{B}{0.01 {\rm G}} \right)^{-3/2}$. We show that
the energetics of the persistent source requires an initial spin period shorter
than 36~ms, and the magnetic field of the neutron star must exceed $4.5\times
10^{12}$~G. This implies that the persistent source does not necessarily
require energetic input from a magnetar.
