  We present 610-MHz Giant Metrewave Radio Telescope observations of 0.84
deg$^2$ of the AMI001 field (centred on $00^{\rm h} 23^{\rm m} 10^{\rm s}$,
$+31^{\circ} 53'$) with an r.m.s. noise of 18 $\mu$Jy beam$^{-1}$ in the centre
of the field. 955 sources are detected, and 814 are included in the source
count analysis. The source counts from these observations are consistent with
previous work. We have used these data to study the spectral index distribution
of a sample of sources selected at 15.7 GHz from the recent deep extension to
the Tenth Cambridge (10C) survey. The median spectral index, $\alpha$, (where
$S \propto \nu^{-\alpha}$) between $0.08 < S_{15.7~\rm GHz} / \rm mJy < 0.2$ is
$0.32 \pm 0.14$, showing that star-forming galaxies, which have much steeper
spectra, are not contributing significantly to this population. This is in
contrast to several models, but in agreement with the results from the 10C
ultra-deep source counts; the high-frequency sky therefore continues to be
dominated by radio galaxies down to $S_{15.7~\rm GHz} = 0.1$ mJy.
