An Improved Transit Measurement for a 2.4 R_{Earth} Planet Orbiting A Bright Mid-M Dwarf K2$-$28

We present a new {\em Spitzer} transit observation of K2$-$28b, a sub-Neptune ($R_{\rm p} = 2.45\pm0.28 R_{Earth}$) orbiting a relatively bright ($V_{\rm mag} = 16.06$, $K_{\rm mag} = 10.75$) metal-rich M4 dwarf (EPIC 206318379). This star is one of only seven with masses less than 0.2 M_{Sun} known to host transiting planets, and the planet appears to be a slightly smaller analogue of GJ 1214b ($2.85\pm0.20 R_{Earth}$; \citealt{2013A&A...549A..10H}). Our new {\em Spitzer} observations were taken two years after the original K2 discovery data and have a significantly higher cadence, allowing us to derive improved estimates for this planet's radius, semi-major axis, and orbital period, which greatly reduce the uncertainty in the prediction of near future transit times for the {\em James Webb Space Telescope} ({\em JWST}) observations. We also evaluate the system's suitability for atmospheric characterization with {\em JWST} and find that it is currently the only small (< 3 R_{Earth}) and cool ($< 600$ K) planet aside from GJ 1214b with a potentially detectable secondary eclipse. We also note that this system is a favorable target for near-infrared radial velocity instruments on larger telescopes (e.g., the Habitable Planet Finder on the Hobby-Eberly Telescope), making it one of only a handful of small, cool planets accessible with this technique. Finally, we compare our results with the simulated catalog of the Transiting Exoplanet Survey Satellite ({\em TESS}) and find K2$-$28b to be representative of the kind of mid-M systems that should be detectible in the {\em TESS} sample.