What war are you talking about ?
The statement that best describes what happened when Constantine tried to establish New Rome is: He was successful in building a new political center in the East, unified by the Christian religion.
Even Until today, the residual of Constantine's territory still remained as the center of the christian culture in the world. We most commonly know it as the Vatican city.
The decline of Olmec society might have been caused by civil conflicts. Conflicts among the citizens of this society are likely to have been the cause of its downfall.