Modular forms reference If f is a weight 2 newform on $\Gamma_1(N)$ then there exists an abelian variety Af whose endomorphism algebra is isomorphic to the field generated by the coefficients of f.
I've seen this proven in Shimura's book, but was wondering if anyone knows of a different reference (perhaps one that is a bit more readable...).
Thanks.
 A: Have a look at Section 6.6 of Diamond and Shurman, A First Course in Modular Forms:
As an aside, the theorem states a bit more than you have said: for instance, when the field of Fourier coefficients is $\mathbb{Q}$, you are just asserting the existence of an elliptic curve $E_{/\mathbb{Q}}$ with $\operatorname{End}_{\mathbb{Q}}(E) \otimes_{\mathbb{Z}} \mathbb{Q} = \mathbb{Q}$: every elliptic curve over $\mathbb{Q}$ has this property.  You want to require an equality of L-series between the abelian variety and the modular form.
A: Just to add one more thing to what Pete said: the variety A_f that one normally attaches to f might have endomorphism ring bigger than an order in the coefficient field of f: for example if E is an elliptic curve with complex multiplication, the associated modular form still only has coefficients in Z. The correct statement is that the endomorphism ring contains an order in the coefficient field
A: The Anterp conference volumes, "Modular functions in one Variable - I, II, III, .... " might contain what you want. I am not sure though, as I am unable to verify it by looking into all the volumes.
