We report on Westerbork 1.4 GHz radio observations of the radio counterpart to \gamma -ray burst GRB 970508 , between 0.80 and 138 days after this event .
The 1.4 GHz light curve shows a transition from optically thick to thin emission between 39 and 54 days after the event .
We derive the slope p of the spectrum of injected electrons ( d N /d \gamma _ { e } \propto \gamma _ { e } ^ { - p } ) in two independent ways which yield values very close to p = 2.2 .
This is in agreement with a relativistic dynamically near-adiabatic blast wave model whose emission is dominated by synchrotron radiation and in which a significant fraction of the electrons cool fast .