  Context. GJ 1148 is an M-dwarf star hosting a planetary system composed of
two Saturn-mass planets in eccentric orbits with periods of 41.38 and 532.02
days. Aims. We reanalyze the orbital configuration and dynamics of the GJ 1148
multi-planetary system based on new precise radial velocity (RV) measurements
taken with CARMENES. Methods. We combined new and archival precise Doppler
measurements from CARMENES with those available from HIRES for GJ 1148 and
modeled these data with a self-consistent dynamical model. We studied the
orbital dynamics of the system using the secular theory and direct N-body
integrations. The prospects of potentially habitable moons around GJ 1148 b
were examined. Results. The refined dynamical analyses show that the GJ 1148
system is long-term stable in a large phase-space of orbital parameters with an
orbital configuration suggesting apsidal alignment, but not in any particular
high-order mean-motion resonant commensurability. GJ 1148 b orbits inside the
optimistic habitable zone (HZ). We find only a narrow stability region around
the planet where exomoons can exist. However, in this stable region exomoons
exhibit quick orbital decay due to tidal interaction with the planet.
Conclusions. The GJ 1148 planetary system is a very rare M-dwarf planetary
system consisting of a pair of gas giants, the inner of which resides in the
HZ. We conclude that habitable exomoons around GJ 1148 b are very unlikely to
exist.
