International Journal of Number Theory
We give a list of PGL2(Fl) number fields for ℓ ≥ 11 which have rational companion forms. Our list has fifty-three fields and seems likely to be complete. Some of the fields on our list are very lightly ramified for their Galois group.
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David P. Roberts. PGL2(Fl) number fields with rational companion forms. International Journal of Number Theory 14 (2018), no. 3, 825-845.