As per PubChem: $pK_1 = 2.18$; $pK_2 = 8.95$; $pK_3 = 10.53$ at 38 °C, indicating that the side chain amino group is deprotonated at a higher pH, indicating it is more basic. I tried to justify this by analysing electronic effects in the conjugate acid:
Attempt I) The carboxylic acid group, at a higher pH would exist as $\ce{-COO}^{-}$ and exert a +I effect on nearby atoms. Then the alpha-amino group should be more stable in the protonated form and be more basic.
Attempt II) The carboxylate anion and $\ce{-NH_3}^{+}$ group may form hydrogen bonds. This again leads me to conclude that the alpha-amino group should be more basic.
But the experimental data contradict this. Perhaps the carboxylate anion H-bonds with (and stabilises) the side-chain amino group instead, but this seems unlikely (9-membered ring?).
Could anyone provide a decent theoretical explanation of the $pKa$ values?