Geodesic
Supersingular elliptic curves, theta series and weight two modular forms
Emerton, Matthew1
1Department of Mathematics, Northwestern University, 2033 Sheridan Rd., Evanston, Illinois 60208-2730
Journal of the American Mathematical Society, Tome 15 (2002) no. 3, pp. 671-714
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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.
DOI : 10.1090/S0894-0347-02-00390-9

Emerton, Matthew  1

1 Department of Mathematics, Northwestern University, 2033 Sheridan Rd., Evanston, Illinois 60208-2730 
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Emerton, Matthew. Supersingular elliptic curves, theta series and weight two modular forms. Journal of the American Mathematical Society, Tome 15 (2002) no. 3, pp. 671-714. doi: 10.1090/S0894-0347-02-00390-9

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