We read in Matt 27 how Jesus was put to trial before the Roman Governor:
Then Pilate said to him, “Do you not hear how many accusations they make against you?” But he gave him no answer, not even to a single charge, so that the governor was greatly amazed......... For he realized that it was out of jealousy that they had handed him over. ....... The governor again said to them, “Which of the two do you want me to release for you?” And they said, “Barabbas.” Pilate said to them, “Then what should I do with Jesus who is called the Messiah?” All of them said, “Let him be crucified!” Then he asked, “Why, what evil has he done?” But they shouted all the more, “Let him be crucified!” So when Pilate saw that he could do nothing, but rather that a riot was beginning, he took some water and washed his hands before the crowd, saying, “I am innocent of this man’s blood; see to it yourselves.”
The charges levelled against Jesus were blasphemy and misleading of the Jews against Roman empire, calling himself their king. The first one would come under Hebrew law and the trial & punishment was of summary nature, as we see in Jn 8:58-59:
Jesus said to them, “Very truly, I tell you, before Abraham was, I am.” So they picked up stones to throw at him, but Jesus hid himself and went out of the temple.
And we see the Jewish leaders saying to Pilate:
The Jews answered him, “We have a law, and according to that law he ought to die because he has claimed to be the Son of God.” (Jn 19:7)
Those days, only the Romans had the power to award death sentence to Jews (Jn 18:31). But blasphemy was not listed by Romans as a crime demanding death sentence.
The second charge could not be substantiated, as we see Pilate putting up the sign of INRI over Jesus' cross, much to the embarrassment of the Jewish leaders (Jn 19:22).
In effect, Jesus was convicted for allegedly breaking Hebrew laws, but was awarded death sentence under Roman laws.
My question therefore, is: Under the laws of which regime was Jesus sentenced to death on the cross? Inputs from any denomination are welcome.