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arXiv · 1508.07916

Modular forms and some cases of the inverse Galois problem

David Zywina
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Abstract

We prove new cases of the inverse Galois problem by considering the residual Galois representations arising from a fixed newform. Specific choices of weight $3$ newforms will show that there are Galois extensions of $\mathbb{Q}$ with Galois group $PSL_2(\mathbb{F}_p)$ for all primes $p$ and $PSL_2(\mathbb{F}_{p^3})$ for all odd primes $p \equiv \pm 2, \pm 3, \pm 4, \pm 6 \pmod{13}$.

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David Zywina. 2015-08-31. Modular forms and some cases of the inverse Galois problem. https://arxiv.org/abs/1508.07916

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