The Bible teaches that God "ministered" to Israel under Law...by the Law and through the Law. After Christ died the Bible teaches God "ministers" to the human heart by the Holy Spirit.
The Holy Spirit was given at Calvary. God's new dispensation of Grace birthed the Church, the body of Christ. Within in the Church is the ministry of the Holy Spirit.
When Jesus rose from the grave and preached to the disciples (before His ascension to Heaven) He commanded the disciples to preach the Gospel. When the Gospel is preached...the Holy Spirit "ministers" to the heart.
Is "repentance" the ministry of the Holy Spirit? Yes. How? When the Gospel is preached it's the goodness of God that "leads" men to repentance. Repentance means to change your mind.
Is "conviction" the ministry of the Holy Spirit? Yes. How? When the Gospel is preached the Holy Spirit "touches or ministers" to the unbelieving soul. This ministry stirs, sways, and causes man to believe. This ministry of the Spirit is what gets mans attention. This ministry of the Spirit is what "testifies and reveals" Christ to the human soul.
The ministry of the Holy Spirit today is what draws men to God. Preaching the Gospel allows God to minister truth and Christ to the hearer. Holy men of God carry the Gospel. Holy men of God minister the Spirit. Holy men of God preach Christ crucified! Holy men of God are ministers...but the Holy Spirit "ministers" the Gospel that we preach.
John 6:44-45...No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day. It is written in the prophets, And they shall be all taught of God. Every man therefore that hath heard, and hath learned of the Father, cometh unto me.
Notice Jesus said under Law that Israel must be taught...they must learn...and they must hear...in order for God to "draw" them. Even more so today in the Grace covenant where the Holy Spirit ministers Salvation to the human soul through the Gospel message. That ministration of the Spirit of God that I speak of "under Grace"... flows straight from Calvary! Glory! That's where forgiveness of sin is found also! How? God ministers forgiveness and removal of guilt to the human conscience through the ministry of the Holy Spirit.