We present the simple effective theory of quark masses, mixing and CP violation
with level N=3 (A4) modular symmetry, which provides solution to the strong CP problem without the need for an axion. The CP symmetry is broken spontaneously by the vacuum expectation value of the modulus tau. This provides the requisite large value of the CKM CP-violating phase while the strong CP phase remains zero or is tiny. Within the considered framework we discuss phenomenologically viable quark mass matrices with texture zeros, which are realized by assigning both the left- and right-handed quark fields to A4 singlets with appropriate modular weights. The VEV of tau is restricted to reproduce the observed CKM parameters.

With support from FCT through project UIDB/00777/2020

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