  Gliese 876 harbors one of the most dynamically rich and well-studied
exoplanetary systems. The nearby M4V dwarf hosts four known planets, the outer
three of which are trapped in a Laplace mean-motion resonance. A thorough
characterization of the complex resonant perturbations exhibited by the
orbiting planets, and the chaotic dynamics therein, is key to a complete
picture of the system's formation and evolutionary history. Here we present a
reanalysis of the system using six years of new radial velocity (RV) data from
four instruments. This new data augments and more than doubles the size of the
decades-long collection of existing velocity measurements. We provide updated
estimates of the system parameters by employing a computationally efficient
Wisdom-Holman N-body symplectic integrator, coupled with a Gaussian Process
(GP) regression model to account for correlated stellar noise. Experiments with
synthetic RV data show that the dynamical characterization of the system can
differ depending on whether a white noise or correlated noise model is adopted.
Despite there being a region of stability for an additional planet in the
resonant chain, we find no evidence for one. Our new parameter estimates place
the system even deeper into resonance than previously thought and suggest that
the system might be in a low energy, quasi-regular double apsidal corotation
resonance. This result and others will be used in a subsequent study on the
primordial migration processes responsible for the formation of the resonant
chain.
