  The Local Group dwarf elliptical galaxy M32 hosts one of the nearest and most
under-luminous super-massive black holes (SMBHs) ever known, offering a rare
opportunity to study the physics of accreting SMBHs at the most quiescent
state. Recent Very Large Array (VLA) observations have detected a radio source
at the nucleus of M32, which is suggested to be the radio counterpart of the
SMBH. To further investigate the radio properties of this nuclear source, we
have conducted follow-up, high-resolution VLA observations in four epochs
between 2015--2017, each with dual frequencies. At 6 GHz, the nuclear source is
resolved under an angular resolution of $\sim$0\farcs4, exhibiting a coreless,
slightly lopsided morphology with a detectable extent of $\sim$2.5 \arcsec
($\sim$10 parsec). No significant variability can be found among the four
epochs. At 15 GHz, no significant emission can be detected within the same
region, pointing to a steep intrinsic radio spectrum (with a 3\,$\sigma$ upper
limit of -1.46 for the spectral index). We discuss possible scenarios for the
nature of this nuclear source and conclude that a stellar origin, in particular
planetary nebulae, X-ray binaries, supernova remnants or diffuse ionized gas
powered by massive stars, can be ruled out.Instead, the observed radio
properties can be explained by synchrotron radiation from a hypothetical wind
driven by the weakly accreting SMBH.
