We know that for every normalized Hecke eigenform $f$, its Fourier coefficients generate a number field. I wonder if we have an "inverse Galois" type conjecture regarding which number fields can be generated in this way. Moreover, do we have some sort of statistical results/conjectures regarding the frequency of a number field appearing as a field generated by the Fourier coefficients of an eigenform? I would like to apologize in advance if this is a naive question.
2026-03-30 12:57:06.1774875426
Number Fields Generated by Fourier Coefficients of Modular Forms
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