  To every hyperelliptic curve one can assign the periods of the integrals over
the holomorphic and the meromorphic differentials. By comparing two
representations of the so-called projective connection it is possible to
reexpress the latter periods by the first. This leads to expressions including
only the curve's parameters $\lambda_j$ and modular forms. By a change of basis
of the meromorphic differentials one can further simplify this expression. We
discuss the advantages of these explicitly given bases, which we call Baker and
Klein basis, respectively.
