Distinguishing newforms

S Chow; A Ghitza

Journal article

Distinguishing newforms

S Chow, A Ghitza

International Journal of Number Theory | WORLD SCIENTIFIC PUBL CO PTE LTD | Published : 2015

DOI: 10.1142/S1793042115500499

Abstract

Let n0(N, k) be the number of initial Fourier coefficients necessary to distinguish newforms of level N and even weight k. We produce extensive data to support our conjecture that if N is a fixed squarefree positive integer and k is large then n0(N, k) is the least prime that does not divide N.

University of Melbourne Researchers

Alex Ghitza Author

Related Projects (1)

Coset spaces and Hecke algebra actions

This project will develop fundamental models and their mechanics as tools for studying subtle geometry and hidden symmetry in number systems..

Grants

Awarded by Engineering and Physical Sciences Research Council

Funding Acknowledgements

Thanks to James Withers for running some of the codes. We also thank David Loeffler, M. Ram Murty, Abhishek Saha, Fredrik Stromberg and the referee for useful comments. The first author was supported by the Elizabeth and Vernon Puzey scholarship, and is grateful towards the University of Melbourne for their hospitality while preparing this memoir. The second author was supported by Discovery Grant DP120101942 from the Australian Research Council.