  We consider a finite dimensional representation of the dihedral group
$D_{2p}$ over a field of characteristic two where $p$ is an odd prime and study
the corresponding Hilbert ideal $I_H$. We show that $I_H$ has a universal Gr\"
{o}bner basis consisting of invariants and monomials only. We provide sharp
bounds for the degree of an element in this basis and in a minimal generating
set for $I_H$. We also compute the top degree of coinvariants.
