  The 21\,cm transition of neutral hydrogen is opening an observational window
into the cosmic dawn of the universe---the epoch of first star formation. We
use 28\,hr of data from the Owens Valley Radio Observatory Long Wavelength
Array (OVRO-LWA) to place upper limits on the spatial power spectrum of 21\,cm
emission at $z \approx 18.4$ ($\Delta_{21} \lesssim 10^4\,\text{mK}$), and
within the absorption feature reported by the EDGES experiment (Bowman et al.
2018). In the process we demonstrate the first application of the double
Karhunen-Lo\`{e}ve transform for foreground filtering, and diagnose the
systematic errors that are currently limiting the measurement. We also provide
an updated model for the angular power spectrum of low-frequency foreground
emission measured from the northern hemisphere, which can be used to refine
sensitivity forecasts for next-generation experiments.
