The Greek word translated faith is “pistis”. The related verb is “pisteuo”. It is often translated as “believe”. In his book called Salvation by Allegiance Alone, Matthew Bates explains that the word “pistis” is much broader than faith, although it sometimes does mean faith. He explains that the pistis has three dimensions.
Bates says that intellectual agreement with the gospel is not enough. God expects allegiance to Jesus.
I would put it this way. The Greek word for faith included the following elements.
Intellectual assent to the truth of the gospel
Jesus is the son of God.
He died on the cross,
rose from the dead
and ascended into the spiritual realms.
He is now seated at the right hand of the father,
far above all spiritual authority.
The person choosing to follow Jesus must believe these facts about Jesus are true. This is belief.
Trust in the reliability of God
We decide to trust God
He can be trusted to do what he says he will do.
He is good, so he will do good things.
He has the power to do what he says he will do.
Transferring allegiance to Jesus
We are saved by giving our full allegiance to Jesus.
We renounce all other loyalties,
to the world and to the spiritual powers of evil.
We give ourselves to be be subjects of Jesus.