  We constrain the X-ray properties of the nearby $(360\,{\rm pc})$, old
($5\,{\rm Myr}$) pulsar B1133+16 with $\sim 100\,{\rm ks}$ effective exposure
time by {\it XMM-Newton}. The observed pulsar flux in the 0.2-3 keV energy
range is $\sim 10^{-14} \, {\rm erg \, cm}^{-2} \, {\rm s}^{-1}$, which results
in the recording of $\sim 600$ source counts with the EPIC pn and MOS
detectors. The X-ray radiation is dominated by nonthermal radiation and is well
described by both a single power-law model (PL) and a sum of blackbody and
power-law emission (BB+PL). The BB+PL model results in a spectral photon index
$\Gamma=2.4^{+0.4}_{-0.3}$ and a nonthermal flux in the 0.2-3 keV energy range
of $(7\pm 2) \times 10^{-15}\, {\rm erg \, cm}^{-2} \, {\rm s}^{-1}$. The
thermal emission is consistent with the blackbody emission from a small hot
spot with a radius of $R_{\rm pc} \approx 14^{+7}_{-5} \, {\rm m}$ and a
temperature of $T_{\rm s} = 2.9^{+0.6}_{-0.4} \, {\rm MK}$. Assuming that the
hot spot corresponds to the polar cap of the pulsar, we can use the magnetic
flux conservation law to estimate the magnetic field at the surface $B_{\rm s}
\approx 3.9 \times 10^{14} \, {\rm G}$. The observations are in good agreement
with the predictions of the partially screened gap model, which assumes the
existence of small-scale surface magnetic field structures in the polar cap
region.
