  The recently detected TRAPPIST-1 planetary system, with its seven planets
transiting a nearby ultracool dwarf star, offers the first opportunity to
perform comparative exoplanetology of temperate Earth-sized worlds. To further
advance our understanding of these planets' compositions, energy budgets, and
dynamics, we are carrying out an intensive photometric monitoring campaign of
their transits with the $\textit{Spitzer Space Telescope}$. In this context, we
present 60 new transits of the TRAPPIST-1 planets observed with
$\textit{Spitzer}$/IRAC in February and March 2017. We combine these
observations with previously published $\textit{Spitzer}$ transit photometry
and perform a global analysis of the resulting extensive dataset. This analysis
refines the transit parameters and provides revised values for the planets'
physical parameters, notably their radii, using updated properties for the
star. As part of our study, we also measure precise transit timings that will
be used in a companion paper to refine the planets' masses and compositions
using the transit timing variations method. TRAPPIST-1 shows a very low level
of low-frequency variability in the IRAC 4.5-$\mu$m band, with a photometric
RMS of only 0.11$\%$ at a 123-s cadence. We do not detect any evidence of a
(quasi-)periodic signal related to stellar rotation. We also analyze the
transit light curves individually, to search for possible variations in the
transit parameters of each planet due to stellar variability, and find that the
$\textit{Spitzer}$ transits of the planets are mostly immune to the effects of
stellar variations. These results are encouraging for forthcoming transmission
spectroscopy observations of the TRAPPIST-1 planets with the $\textit{James
Webb Space Telescope}$.
