$PGL_2(\mathbb{F}_\ell)$ number fields with rational companion forms

preprint2016arXivOpen access

We give a list of $PGL_2(\mathbb{F}_\ell)$ number fields for $\ell \geq 11$ 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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$PGL_2(\mathbb{F}_\ell)$ number fields with rational companion forms

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PGL2(Fℓ)PGL_2(\mathbb{F}_\ell)PGL2​(Fℓ​) number fields with rational companion forms

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$PGL_2(\mathbb{F}_\ell)$ number fields with rational companion forms