  For the $p$-dimensional filiform Lie algebra ${\mathfrak m}_2(p)$ over a
field ${\mathbb F}$ of prime characteristic $p\ge 5$ with nonzero Lie brackets
$[e_1,e_i] = e_{i+1}$ for $1<i<p$ and $[e_2,e_i]=e_{i+2}$ for $2<i<p-1$, we
show that there is a family ${\mathfrak m}_2^{\lambda}(p)$ of restricted Lie
algebra structures parameterized by elements $\lambda \in {\mathbb F}^p$. We
explicitly describe bases for the ordinary and restricted 1- and 2-cohomology
spaces with trivial coefficients, and give formulas for the bracket and
$[p]$-operations in the corresponding restricted one-dimensional central
extensions.
