The mod 4 behaviour of total Lie algebra cohomology

We show that if L is a unimodular Lie algebra over a field of characteristi c not equal 2, then the dimension sigma (L) of the total cohomology of L is a multiple of 4 when dim(L) not equivalent to 3 (mod 4). However, contrary to a claim by Deninger and Singhof, we give an example of a rational nilpo tent algebra L of dimension 15 with sigma (L) not equivalent to 0 (mod 4). Over fields of characteristic 2, we completely classify those algebras L wi th sigma (L) not equivalent to 0 (mod 4).