The quadrupole moments of the upsilon i_13/2 intruder bands in ^135,135Sm have been deduced from nuclear lifetimes measured using the Doppler shift attenuation method. A centroid shift analysis of the data yielded values of Q₀=7.0 eb and 5.0 eb for ¹³⁵Sm and ¹³⁷Sm respectively. The value for the band in ¹³⁵Sm is the largest yet measured for an odd-N nucleus in this mass region and is consistent with the deformations of superdeformed (SD) bands in this mass region. This implies that the odd-N SD and single upsilon i_13/2 intruder bands wound mass 135 are all based on the same single particle configuration, upsilon 6¹. In addition, a lineshape analysis has been performed on the ¹³⁵Sm data in order to assess the nature of the sidefeeding into the band. The results indicate a value for the static quadrupole moment which is consistent with that obtained using the centroid shift method. There is little evidence of any significantly slow sidefeeding component in the lineshapes.