Modular Forms on Noncongruence Subgroups and Atkin–Swinnerton-Dyer Relations

Liqun Fang, J. William Hoffman, Benjamin Linowitz, Andrew Rupinski, Helena Verrill

Type: Article

Publication Date: 2010-01-01

Citations: 13

DOI: https://doi.org/10.1080/10586458.2010.10129064

Abstract

We give new examples of noncongruence subgroups Γ ⊂ SL2(ℤ) whose space of weight-3 cusp forms S 3(Γ) admits a basis satisfying the Atkin–Swinnerton-Dyer congruence relations with respect to a weight-3 newform for a certain congruence subgroup.

Locations

Experimental Mathematics - View
arXiv (Cornell University) - View - PDF
Project Euclid (Cornell University) - View - PDF

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+ PDF Chat	On the Hecke Algebra of a Noncongruence Subgroup	1997	A. J. Scholl
+	Introduction to the Arithmetic Theory of Automorphic Functions	1972	Marvin Tretkoff Goro Shimura
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