Journal of the American Mathematical Society

Author(s): Matthew Emerton
Journal: J. Amer. Math. Soc. 15 (2002), 671-714.
MSC (2000): Primary 11F11, 11F27, 11F37
Posted: February 27, 2002
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Abstract: Let

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

, at infinity, and at no other primes.

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