Why do Catholics not sing the Gloria or alleluia during Lent?

Alleluia means praise to God, sung with great joy. Lent is a time for penance and a reminder of our sinfulness and the hope of everlasting life. So we do not say alleluia, but we do sing praise to God. Then on Easter, a time of great joy, we sing alleluia again ( in fact, twice at the closing of Mass)