  We present here a detailed spectral study of the X-ray emission of the
persistent source and the low-fluence bursts of SGR J0501+4516 observed during
a deep XMM-Newton observation near the peak of its 2008 outburst. For the
persistent emission we employ a physically motivated continuum emission model
and spectroscopically determine important source properties; such as, the
surface magnetic field strength and the magnetospheric scattering optical
depth. We find that the magnetar surface temperature near the peak of its
activity is 0.38 keV, corresponding to an emission area of 131 km^2 at a
distance of 2 kpc. The surface magnetic field strength determined
spectroscopically, B=2.2E14 G, is consistent with the dipole field strength
inferred from the source spin and spin down rate. We fit the stacked spectra of
129 very faint bursts with a modified blackbody model and find a temperature of
1.16 keV, corresponding to an emission area of 93 km^2. We also find an
evidence for cooling during the burst decay phase.
