Moduli stabilization in finite modular symmetric models

We study vacua of moduli potential consisting of multiple contribution of modular forms in a finite modular symmetry. If the potential is given by a single modular form, the Minkowski vacuum is realized at the fixed point of the modular symmetry. We show that the de Sitter vacuum is realized with a multiple modular form case and obtain a non-trivial vacuum which is away from the fixed point, i.e. a large modulus vacuum expectation value, depending on the choice of the weight and representation of the modular forms. We study these vacua numerically and analytically. It is also found that the vacua obtained in this paper preserve CP symmetry.