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arXiv · 1503.02767

Hecke algebras, new vectors and new forms on $Γ_0(m)$

Ehud Moshe Baruch·Soma Purkait
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Abstract

We characterize the space of new forms for $Γ_0(m)$ 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 $K={\rm GL}_2(\mathbb{Z}_p)$. 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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Ehud Moshe Baruch, Soma Purkait. 2015-03-10. Hecke algebras, new vectors and new forms on $Γ_0(m)$. https://arxiv.org/abs/1503.02767

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