Any reference on Eisenstein Series for $\Gamma_0(N)$ in $\mathrm{GL}(2)$ What is the best reference on Eisenstein Series for $\Gamma_0(N)$ in $\mathrm{GL}(2,\mathbb{R})$?
For fixed $\Gamma_0(N)$, should there be several Eisenstein series (corresponding to each cusp)?
 A: For detailed information I recommend "Chapter 7. Eisenstein series" in Miyake: Modular Forms (Springer Verlag, 2006).
A: Miyake, already recommended by GH, is a very complete reference, which is perhaps the only place to contain complete proofs about the subject. However, for that reason, and also because
he works with weird modular groups $\Gamma_1(a,b)$ conjugate to but not equal to 
the more familiar $\Gamma_1(ab)$, it is difficult to read.
So I propose another reference which contains a clear complete basis of
Eisenstein series, which are eigenforms for $\Gamma_1(N)$, together with their nebentypus,
and their Hecke eigenvalues : W. Stein, Modular Forms, A Computational Approach, available at
http://wstein.org/books/modform/modform/index.html
. More precisely, see here.
To get Eisenstein series for $\Gamma_0(N)$ from those for $\Gamma_1(N)$, just restrict to those with trivial nebentypus, that is $\psi \chi=1$ in the notation of the reference given.
And about your question: in weight $>2$, there are as many independent Eisenstein series
as cusps; in weight $2$, the dimension of the Eisenstein subspace is the number of cusp minus 1, because "$E_2$ is missing". 
