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arXiv · 1808.04588

Newforms mod p in squarefree level, with applications to Monsky's Hecke-stable filtration

Shaunak V. Deo·Anna Medvedovsky·Alexandru Ghitza
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Abstract

We propose an algebraic definition of the space of l-new mod-p modular forms for Gamma0(Nl) in the case that l is prime to N, which naturally generalizes to a notion of newforms modulo p in squarefree level. We use this notion of newforms to interpret the Hecke algebras on the graded pieces of the space of mod-2 level-3 modular forms described by Paul Monsky. Along the way, we describe a renormalized version of the Atkin-Lehner involution: no longer an involution, it is an automorphism of the algebra of modular forms, even in characteristic p.

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Shaunak V. Deo, Anna Medvedovsky, Alexandru Ghitza. 2018-08-14. Newforms mod p in squarefree level, with applications to Monsky's Hecke-stable filtration. https://arxiv.org/abs/1808.04588

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