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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Supersingular elliptic curves, theta series and weight two modular forms
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by Matthew Emerton
J. Amer. Math. Soc. 15 (2002), 671-714
Published electronically: February 27, 2002


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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Bibliographic Information
  • Matthew Emerton
  • Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Rd., Evanston, Illinois 60208-2730
  • Email:
  • Received by editor(s): November 1, 2000
  • Received by editor(s) in revised form: September 19, 2001
  • Published electronically: February 27, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 15 (2002), 671-714
  • MSC (2000): Primary 11F11, 11F27, 11F37
  • DOI:
  • MathSciNet review: 1896237