Why was the construction of the Hagia Sophia so important for Justinian?

Emperor Justinian considered himself the patron saint of all Christians, and he considered Byzantium the stronghold and protector of the entire Christian world. The construction of the Hagia Sophia was supposed to clearly prove this. This temple itself was one of the greatest works of architecture that has survived to this day (albeit as a mosque). Justinian, realizing the scale of construction and its significance, rightfully hoped that his name would be glorified in the centuries as one of the greatest builders.