Jurors could soon begin deliberating over whether a former Hawaii-based soldier convicted of murder should be sentenced to death.

Closing arguments are scheduled Thursday in the sentencing eligibility phase of the Naeem Williams trial. Deliberations are expected to follow.

The jury last month convicted Williams in the 2005 beating death of his 5-year-old daughter, Talia.

Williams faces the death penalty even though Hawaii abolished capital punishment in 1957. Because the crime took place on military property, the case is in the federal justice system, which allows for the death penalty.

The sentencing hearings have been ongoing for several weeks, with experts testifying about Williams’ low IQ. The defense is trying to show that his low level of intelligence doesn’t make him eligible for a death sentence.