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Supersingular elliptic curves, theta series and weight two modular forms


Author: Matthew Emerton
Journal: J. Amer. Math. Soc. 15 (2002), 671-714
MSC (2000): Primary 11F11, 11F27, 11F37
DOI: https://doi.org/10.1090/S0894-0347-02-00390-9
Published electronically: February 27, 2002
MathSciNet review: 1896237
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Abstract: Let $p$ be a prime, and let $\mathcal {M}$ denote the space of weight two modular forms on $\Gamma _{0}(p)$ all of whose Fourier coefficients are integral, except possibly for the constant term, which should be either integral or half-integral. We prove that $\mathcal {M}$ is spanned as a $\mathbb {Z}$-module by theta series attached to the unique quaternion algebra that is ramified at $p$, at infinity, and at no other primes.


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Additional Information

Matthew Emerton
Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Rd., Evanston, Illinois 60208-2730
Email: emerton@math.northwestern.edu

Received by editor(s): November 1, 2000
Received by editor(s) in revised form: September 19, 2001
Published electronically: February 27, 2002
Article copyright: © Copyright 2002 American Mathematical Society