  We use the large scale nuclear shell model to calculate the nuclear matrix
elements for the neutrino mediated neutrinoless double beta decay within the
Left-Right symmetric model for four nuclei: $^{76}$Ge, $^{82}$Se, $^{130}$Te
and $^{136}$Xe. We perform a systematic analysis on the general magnitude of
different terms for related mechanisms. For the $\eta$ mechanism, we find that
the weak magnetism $R$ term dominates the decay rate while the $p$-wave effect
is suppressed. While for the $\lambda$ mechanism, the $\omega$ and the $q$
terms are with equal importance. For the latter $q$ term, important
contributions from weak-magnetism MM part are observed. Finally, we give the
constraints on the new physics parameters $m_{\beta\beta}$, $\lambda$ and
$\eta$ from current experiments.
