  This paper is a natural continuation of a joint paper with Bajpai, Harder and
Moya Giusti \cite{BHHM}, even though it began as an answer to Goncharov's
question. It that paper, we had complete description for all representations
except for odd symmetric powers and their dual ones. For those representations
we were left with two options: certain one dimensional module is a ghost space
or not. Here we find the $H^2(SL_3(\Z),V_3)$ has ghost classes. It means that
it is generated by a class from the cohomology of the Borel subgroup.
  With the techniques developed here, we show that the $d_2$ map of the
spectral sequence for the boundary cohomology of $GL_4(\Z)$ is non-trivial if
and only if there is a ghost class in $GL_3(\Z)$ (see Propositions 11 and 12.)
We use a result of Elbaz-Vincent, Gangl and Soule to show that a spectral
sequence related to $GL_4(\Z)$ does not degenerate at $E_2$-level. Then $d_2$
is non-trivial. Therefore, we obtain that $H^2(SL_3(\Z),V_3))$ is a ghost
space, where $V_3$ is the standard representation.
