  We discuss bases of the space of holomorphic quadratic differentials that are
dual to the differentials of Fenchel-Nielsen coordinates and hence appear
naturally when considering functions on the set of hyperbolic metrics which are
invariant under pull-back by diffeomorphisms, such as eigenvalues of the
Laplacian. The precise estimates derived in the current paper form the basis
for the proof of the sharp eigenvalue estimates on degenerating surfaces
obtained in arXiv:1701.08491.
