  Frequencies of acoustic and mixed modes in red giant stars are now determined
with high precision thanks to the long continuous observations provided by the
NASA Kepler mission. Here we consider the eigenfrequencies of nineteen
low-luminosity red giant stars selected by Corsaro et al. (2015) for a detailed
peak-bagging analysis. Our objective is to obtain stellar parameters by using
individual mode frequencies and spectroscopic information. We use a forward
modelling technique based on a minimization procedure combining the frequencies
of the p modes, the period spacing of the dipolar modes, and the spectroscopic
data. Consistent results between the forward modelling technique and values
derived from the seismic scaling relations are found but the errors derived
using the former technique are lower. The average error for log g is 0.002 dex,
compared to 0.011 dex from the frequency of maximum power and 0.10 dex from the
spectroscopic analysis. Relative errors in the masses and radii are on average
2 and 0.5 per cent respectively, compared to 3 and 2 per cent derived from the
scaling relations. No reliable determination of the initial helium abundances
and the mixing length parameters could be made. Finally, for our grid of models
with a given input physics, we found that low-mass stars require higher values
of the overshooting parameter.
