  The \(v\)-function appears in the wild McKay correspondence and it is an
invariant of a Galois extension over a local field which measures about the
ramification of extension. The ramification filtration is also such invariant.
Yasuda presented the problem whether the \(v\)-function is determined by
ramification filtration. In this paper, we give a formula for the
\(v\)-function for 2-dimensional representations of the bicyclic group of order
\(p^2\) with \(p\) the characteristic of our base field. Using this formula, we
construct an example of \(v\)-function not determined by the ramification
filtration.
