  Let $G$ be a filtered Lie conformal algebra whose associated graded conformal
algebra is isomorphic to that of general conformal algebra $gc_1$. In this
paper, we prove that $G\cong gc_1$ or ${\rm gr\,}gc_1$ (the associated graded
conformal algebra of $gc_1$), by making use of some results on the second
cohomology groups of the conformal algebra $\fg$ with coefficients in its
module $M_{b,0}$ of rank 1, where $\fg=\Vir\ltimes M_{a,0}$ is the semi-direct
sum of the Virasoro conformal algebra $\Vir$ with its module $M_{a,0}$.
Furthermore, we prove that ${\rm gr\,}gc_1$ does not have a nontrivial
representation on a finite $\C[\partial]$-module, this provides an example of a
finitely freely generated simple Lie conformal algebra of linear growth that
cannot be embedded into the general conformal algebra $gc_N$ for any $N$.
