I respectfully disagree with the response above. Although agriculture was necessary to feed the populace of Byzantium, it is incorrect to state that the economic foundation of the Empire was agriculture. In fact, its most important economic foundation was trade and the production of fine items made of glass, wool, jewelry, silverware and goldware and especially silk textiles. Its geographic location, midpoint between East and West made the markets of Constantinople quite wealthy; it was in fact the leading spice market of Europe. It was the tremendous wealth generated by Constantinople's spice trade that induced Portugal, Spain and other European countries to seek routes to Asia by which they could bypass the Byzantine merchants. So successful was trade in Constantinople that it was considered the richest city in the known world. Its residents typically simply referred to it as "the city." This term, ist im polis in the Greek of the time was corrupted by the Turks to give the city its present name: Istanbul. So pervasive was the influence of Byzantine trade that its coin, the Bezant, was standard currency in the Mediterranean basin for over five hundred years.
Even more precious than trade to Byzantium was silk production. Byzantium was the chief supplier of silk in the Mediterranean basin. So important was its production that it was carefully supervised by the government, such that no one person could perform more than one step in its production; this to prevent the development of a silk monopoly.
Byzantine trade also led to the development of banking in the area. Banking was not new; however Byzantine merchants used it far more effectively than had previously occurred.
In the time that the Byzantine Empire existed, the economic foundation of any state was agriculture. This was a time when there was very little mechanization and the vast majority of all people were farmers. Therefore, the true economic foundation of the empire was agriculture.
However, the Byzantine Empire also relied quite heavily on trade. The empire was located in the perfect place to control trade between Europe and Asia. All of the trade in things like silks and spices went through the empire and the empire profited greatly from that trade.
So, there were two things that might be seen as the foundations of the empire--agriculture and trade. It seems likely that the answer you are looking for is trade because history books tend to overlook agriculture since it was the basis of all economies.