  Suppose the ground field $\mathbb{F}$ is an algebraically closed field of
characteristic different from 2, 3. We determine the Betti numbers and make a
decomposition of the associative superalgebra of the cohomology for the model
filiform Lie superalgebra. We also describe the associative superalgebra
structures of the (divided power) cohomology for some low-dimensional filiform
Lie superalgebras.
