Abstract
We present new examples of PGL2(F7) and PSL2(F7) number fields ramified at a single prime. To find these number fields we employ the following methods: (i) Specializing a modification of Malle's PGL2(F7) polynomial, (ii) Modular method: computation of Katz modular forms of weight one over F‾7 with prime level, and (iii) Searching for polynomials with prescribed ramification.Method (i) quickly generates many PGL2(F7) number fields unramified at 7 including those fields ramified at only a single prime. Method (ii) can be used to show the existence of PGL2(F7) or PSL2(F7) number fields ramified only at primes that divide the level; we can then use method (iii) to find polynomials for those fields in many cases.
Published Version
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