Trace forms of G-Galois algebras in virtual cohomological dimension 1 and 2

Let G be a finite group and let k be a field of char(k) not equal 2. We explicitly describe the set of trace forms of G-Galois algebras over k when the virtual 2-cohomological dimension vcd(2)(k) of k is at most 1. For fields with vcd(2)(k) less than or equal to 2 we give a cohomological criterion for the orthogonal sum of a trace form of a G-Galois algebra with itself to be isomorphic to another such form.