Hecke algebras, new vectors and new forms on Γ₀(m)

2015/03/10 by Baruch, Ehud Moshe, Purkait, Soma
#11F11 #11F41 #22E50 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1503.02767

Abstract

We characterize the space of new forms for Γ₀(m) as a common eigenspace of certain Hecke operators which depend on primes p dividing the level m. To do that we find generators and relations for a p-adic Hecke algebra of functions on K=\rm GL₂(ℤ_p). We explicitly find the n+1 irreducible representations of K which contain a vector of level n including the unique representation that contains the "new vector" at level n. After translating the p-adic Hecke operators that we obtain into classical Hecke operators we obtain the results about the new space mentioned above.

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