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arXiv · 1810.02134

On higher congruences between cusp forms and Eisenstein series. II

Bartosz Naskręcki
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Abstract

We study congruences between cuspidal modular forms and Eisenstein series at levels which are square-free integers and for equal even weights. This generalizes our previous results from Naskr\k{e}cki [17] for prime levels and provides further evidence for the sharp bounds obtained under restrictive ramification conditions. We prove an upper bound on the exponent in the general square-free situation and also discuss the existence of the congruences when the coefficients belong to the rational numbers and weight equals 2.

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Bartosz Naskręcki. 2018-10-04. On higher congruences between cusp forms and Eisenstein series. II. https://arxiv.org/abs/1810.02134

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