  We consider Stokes water waves on the vorticity flow in a two-dimensional
channel of finite depth. In the paper "V.Kozlov, On first subharmonic
bifurcations in a branch of Stokes waves, JDE, 2024," it was proved existence
of subharmonic bifurcations on a branch of Stokes waves. Such bifurcations
occur near the first bifurcation in the set of Stokes waves. Moreover it is
shown in that paper that the bifurcating solutions build a connected continuum
containing large amplitude waves. This fact was proved under a certain
assumption concerning the second eigenvalue of the Frechet derivative. In this
paper we investigate this assumption and present explicit conditions when it is
satisfied.
