The Lockman Hole is a well-studied extragalactic field with extensive multi-band ancillary data covering a wide range in frequency, essential for characterising the physical and evolutionary properties of the various source populations detected in deep radio fields (mainly star-forming galaxies and AGNs). In this paper we present new 150-MHz observations carried out with the LOw Frequency ARray (LOFAR), allowing us to explore a new spectral window for the faint radio source population. This 150-MHz image covers an area of 34.7 square degrees with a resolution of 18.6$times$14.7 arcsec and reaches an rms of 160 $mu$Jy beam$^{-1}$ at the centre of the field. As expected for a low-frequency selected sample, the vast majority of sources exhibit steep spectra, with a median spectral index of $alpha_{150}^{1400}=-0.78pm0.015$. The median spectral index becomes slightly flatter (increasing from $alpha_{150}^{1400}=-0.84$ to $alpha_{150}^{1400}=-0.75$) with decreasing flux density down to $S_{150} sim$10 mJy before flattening out and remaining constant below this flux level. For a bright subset of the 150-MHz selected sample we can trace the spectral properties down to lower frequencies using 60-MHz LOFAR observations, finding tentative evidence for sources to become flatter in spectrum between 60 and 150 MHz. Using the deep, multi-frequency data available in the Lockman Hole, we identify a sample of 100 Ultra-steep spectrum (USS) sources and 13 peaked spectrum sources. We estimate that up to 21 percent of these could have $z>4$ and are candidate high-$z$ radio galaxies, but further follow-up observations are required to confirm the physical nature of these objects.
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