We study the dynamic susceptibility chi_{T}(Q,t) of deeply supercooled water by means of quasielastic neutron scattering and molecular dynamics simulations. Both techniques show an increase in the peak height of chi_{T}(Q,t) as the temperature is lowered toward the dynamic crossover temperature T_{L} . Below T_{L} , the peak height decreases steadily. We attribute this phenomenon to the change in slope of the Arrhenius plot of the translational relaxation time at T_{L} . In contrast, the peak height of the calculated four-point correlation function chi_{4}(Q,t) , directly related to the size of dynamic heterogeneity, increases toward and below T_{L} .