  K2-146 is a mid-M dwarf ($M_\star = 0.331 \pm 0.009 M_\odot$; $R_\star =
0.330 \pm 0.010 R_\odot$), observed in Campaigns 5, 16, and 18 of the K2
mission. In Campaign 5 data, a single planet was discovered with an orbital
period of $2.6$~days and large transit timing variations due to an unknown
perturber. Here we analyze data from Campaigns 16 and 18, detecting the
transits of a second planet, c, with an orbital period of $4.0$~days, librating
in a 3:2 resonance with planet b. Large, anti-correlated timing variations of
both planets exist due to their resonant perturbations. The planets have a
mutual inclination of $2.40^\circ\pm0.25^\circ$, which torqued planet c more
closely into our line-of-sight. Planet c was grazing in Campaign 5 and thus
missed in previous searches; in Campaigns 16 and 18 it is fully transiting, and
its transit depth is three times larger. We improve the stellar properties
using data from Gaia DR2, and using dynamical fits find that both planets are
sub-Neptunes: their masses are $5.77\pm0.18$ and $7.50\pm0.23 M_{\oplus}$ and
their radii are $2.04\pm0.06$ and $2.19\pm0.07$ R$_\oplus$, respectively. These
mass constraints set the precision record for small exoplanets (a few gas
giants have comparable relative precision). These planets lie in the
photoevaporation valley when viewed in Radius-Period space, but due to the
low-luminosity M-dwarf host star, they lie among the atmosphere-bearing planets
when viewed in Radius-Irradiation space. This, along with their densities being
60%-80% that of Earth, suggests that they may both have retained a substantial
gaseous envelope.

Earth and Planetary Astrophysics