nt.number theory - Modular forms reference

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.

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