Pentecost is both a day and a season. The Day of Pentecost, 50 days after Easter, marks the outpouring of the Holy Spirit on the church. The season of Pentecost is the longest season of the entire Christian Year, stretching out until Advent begins again. Its emphasis is on the work of the Holy Spirit to give power and growth to the church so that the kingdom of God can be built. This season historically concludes with "Christ the King Sunday" which is the last Sunday before the beginning of Advent.
Some possible Psalms to use for Pentecost: