“…The S-matrix and T -matrix of modular fusion categories (see section 2), which reflect many important properties of modular fusion categories, also enjoy interesting algebraic and arithmetic properties [3,4,6]. Therefore, modular fusion categories are inseparable with algebraic number theory and representations of the modular group SL(2, Z) [3,4,10], in particular, one can peer into their properties by considering the number of Galois orbits of the simple objects [16,23] and the representation type of SL(2, Z) associated to a modular category [17], for example.…”