31 Hence also, in the number of the large fishes which our Lord after His resurrection, showing this new life, commanded to be taken on the right side of the ship, there is found the number 50 three times multiplied, with the addition of three more [the symbol of the Trinity] to make the holy mystery more apparent; and the disciples' nets were not broken, because in that new life there shall be no schism caused by the disquiet of heretics. Then [in this new life] man, made perfect and at rest, purified in body and in soul by the pure words of God, which are like silver purged from its dross, seven times refined, shall receive his reward, the denarius; so that with that reward the numbers 10 and 7 meet in him. For in this number there is found, as in other numbers representing a combination of symbols, a wonderful mystery. Nor is it without good reason that the seventeenth Psalm is the only one which is given complete in the book of Kings, because it signifies that kingdom in which we shall have no enemy. For its title is, “A Psalm of David, in the day that the Lord delivered him from the hand of all his enemies, and from the hand of Saul.” For of whom is David the type, but of Him who, according to the flesh, was born of the seed of David? He in His Church, that is, in His body, still endures the malice of enemies. Therefore the words which from heaven fell upon the ear of that persecutor whom Jesus slew by His voice, and whom He transformed into a part of His body (as the food which we use becomes a part of ourselves), were these, “Saul, Saul, why do you persecute Me?” And when shall this His body be finally delivered from enemies? Is it not when the last enemy, Death, shall be destroyed? It is to that time that the number of the 153 fishes pertains. For if the number 17 itself be the side of an arithmetical triangle, formed by placing above each other rows of units, increasing in number from 1 to 17, the whole sum of these units is 153: since 1 and 2 make 3; 3 and 3, 6; 6 and 4, 10; 10 and 5, 15; 15 and 6, 21; and so on: continue this up to 17, the total is 153.
32. The celebration of Easter and Pentecost is therefore most firmly based on Scripture. As to the observance of the forty days before Easter, this has been confirmed by the practice of the Church; as also the separation of the eight days of the neophytes, in such order that the eighth of these coincides with the first. The custom of singing the Alleluia on those 50 days only in the Church is not universal; for in other places it is sung also at various other times, but on these days it is sung everywhere. Whether the custom of standing at prayer on these days and on all the Lord's days, is everywhere observed or not, I do not know; nevertheless, I have told you what guides the Church in this usage, and it is in my opinion sufficiently obvious.
Source: Letters (New Advent)