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A<sc>bstract</sc> The so-called Golden Mass Relation provides a testable correlation between charged-lepton and down-type quark masses, that arises in certain flavor models that do not rely on Grand Unification. Such models typically involve broken family symmetries. In this work, we demonstrate that realistic fermion mass relations can emerge naturally in modular invariant models, without relying onad hocflavon alignments. We provide a model-independent derivation of a class of mass relations that are experimentally testable. These relations are determined by both the Clebsch-Gordan coefficients of the specific finite modular group and the expansion coefficients of its modular forms, thus offering potential probes of modular invariant models. As a detailed example, we present a set of viable mass relations based on the Γ₄≅S₄symmetry, which have calculable deviations from the usual Golden Mass Relation. 

A bstract The Kähler potentials of modular symmetry models receive unsuppressed contributions which may be controlled by a flavor symmetry, where the combination of the two symmetry types is referred to as eclectic flavor symmetry. After briefly reviewing the consistency conditions of eclectic flavor symmetry models, including those with generalised (g)CP, we perform a comprehensive bottom-up study of eclectic flavor symmetry models based on Ω(1) ≅ ∆(27) ⋊ T ′, consisting of the flavor symmetry ∆(27) in a semi-direct product with the modular symmetry T ′. The modular transformations of different ∆(27) multiplets are given by solving the consistency condition. The eight nontrivial singlets of ∆(27) are related by T ′ modular symmetry, and they have to be present or absent simultaneously in any Ω(1) model. The most general forms of the superpotential and Kähler potential invariant under Ω(1) are discussed, and the corresponding fermion mass matrices are presented. Based on the eclectic flavor group Ω(1), two concrete lepton models which can successfully describe the experimental data of lepton masses and mixing parameters are constructed. For the two models without gCP, all six mixing parameters vary in small regions. A nearly maximal atmospheric mixing angle θ 23 and Dirac CP phase δ CP are obtained in the first model. After considering the compatible gCP symmetry and the assumption of $$ \mathfrak{R}\tau $$ R τ = 0 in the first model, the μ − τ reflection symmetry is preserved in the charged lepton diagonal basis. As a consequence, the atmospheric mixing angle and Dirac CP phase are predicted to be maximal, and two Majorana CP phases are predicted to be π .