Tenth Algorithmic Number Theory Symposium ANTS-X University of California, San Diego July 9 – 13, 2012 Tenth Algorithmic Number Theory Symposium (ANTS-X) July 9 – 13, 2012

The impact of computing on noncongruence modular forms

Wen-Ching Winnie Li

Abstract: The arithmetic of modular forms for congruence subgroups is well-understood, after being studied for over one century. Despite the fact that there are far more noncongruence subgroups than congruence subgroups in SL(2,Z), the modular forms for noncongruence subgroups have not attracted broad attention. One main reason is the lack of effective tools. Consequently, its development is much guided by numerical data. In this talk I shall survey the progress on the arithmetic of noncongruence modular forms, explaining how computational results impact theoretical developments of the subject.

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