  We perform a multifractal analysis of homological growth rates of oriented
geodesics on hyperbolic surfaces. Our main result provides a formula for the
Hausdorff dimension of level sets of prescribed growth rates in terms of a
generalized Poincar\'e exponent of the Fuchsian group. We employ symbolic
dynamics developed by Bowen and Series, ergodic theory and thermodynamic
formalism to prove the analyticity of the dimension spectrum.
