 Arf invariant of a quadratic form

For a nonsingular quadratic form over ${\mathbb{F}}_2$ with symplectic basis $(e_i,f_i)$, the invariant is ${\sum }_{i}Q(e_i)Q(f_i)$. For fixed polar form in dimension $2m$, the two types have $2^{m-1}(2^m+1)$ and $2^{m-1}(2^m-1)$ forms.