© 2002-2011 IEEE. The U.S. large hadron collider (LHC) Accelerator Research Program, in close collaboration with The European Organization for Nuclear Research (CERN), has developed three generations of high-gradient quadrupole (HQ) Nb3Sn model magnets, to support the development of the 150 mm aperture Nb3Sn quadrupole magnets for the high-luminosity LHC. The latest generation, HQ03, featured coils with better uniformity of coil dimensions and properties than the earlier generations. The HQ03 magnet was tested at fermi national accelerator laboratory (FNAL), including the field quality study. The profiles of low-order harmonics along the magnet aperture observed at 15 kA, 1.9 K can be traced back to the assembled coil pack before the magnet assembly. Based on the measured harmonics in the magnet center region, the coil block positioning tolerance was analyzed and compared with earlier HQ01 and HQ02 magnets to correlate with coil and magnet fabrication. To study the capability of correcting the low-order nonallowed field errors, magnetic shims were installed in HQ03. The expected shim contribution agreed well with the calculation. For the persistent-current effect, the measured a4 can be related to 4% higher in the strand magnetization of one coil with respect to the other three coils. Finally, we compare the field errors due to the interstrand coupling currents between HQ03 and HQ02.