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Group III Final Presentation
Agenda
1. Congruences of newforms with newforms arising from elliptic curves
2. (Ir)reducibility testing and Serre levels
3. S_4 number fields arising from elliptic curves
4. Period lattices
computing splitting field of modular mod p reps
5. Elliptic curves whose Galois representations are surjective mod 4 (resp. 8) but not mod 2 (resp. 4)