The concept of death is the time when the spirit of man leaves his earthly body. "Do not put your trust in princes, nor in a son of man, in whom there is no help. His spirit departs, he returns to his earth; in that very day his plans perish" (Psalms 146:3-4). "Remember your Creator before the silver cord is loosed, or the golden bowl is broken, or the pitcher shattered at the fountain, or the wheel broken at the well. Then the dust will return to the earth as it was, and the spirit will return to God who gave it" (Ecclesiastes 12:6-7).
Jesus told the thief on the cross, "Assuredly, I say to you, today you will be with Me in Paradise" (Luke 23:42). So, Jesus' soul did not remain with his body, but he went to realm of the dead. Specifically the part that is known as Paradise (Luke 16:19-31).
Peter mentions this in his first sermon when he quoted a Old Testament prophecy: "For You will not leave my soul in Hades, nor will You allow Your Holy One to see corruption" (Acts 2:27). Thus Jesus' soul was not with his body but was in the realm called Hades.