  Denote m_0 the infinite dimensional N-graded Lie algebra defined by basis
e_i, i>= 1 and relations [e_1,e_i] = e_(i+1) for all i>=2. We compute in this
article the bracket structure on H1(m_0,m_0), H2(m_0,m_0) and in relation to
this, we establish that there are only finitely many true deformations of m_0
in each nonpositive weight, by constructing them explicitely. It turns out that
in weight 0 one gets exactly the other two filiform Lie algebras.
