Well-poised hypergeometric data at λ=-1 yield degree-four Galois representations that are automorphic, with traces equal to products of Fourier coefficients of two explicit modular forms.
Transcendence of 3F2(1) hypergeometric series and L-values of modular forms, (preprint) 2024
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The Explicit Hypergeometric-Modularity Method II
Well-poised hypergeometric data at λ=-1 yield degree-four Galois representations that are automorphic, with traces equal to products of Fourier coefficients of two explicit modular forms.