nt.number theory - The convergence of Eisenstein series of weight zero

Consider Eisenstein series of weight zero, i.e.

$ E_{mathfrak{a}}(z, s, chi) = sum_{ gamma in Gamma_{mathfrak{a}} backslash Gamma } bar{chi}(gamma) (Imsigma_{mathfrak{a}}^{-1}
gamma z)^s $,

where $chi$ is a multiplier system of weight zero ( $ chi : Gamma rightarrow mathbb{C}^* $ is a group homomorphism) singular at cusp $mathfrak{a}$. Then my first question is that why this series converges absolutely in $Re(s)>1$?

My second question is how to calculate the following summation:

$ sum_{d (mod c)} epsilon_d(frac{c}{d}) $, where $ gamma = $
$[
begin{pmatrix}
a & b\
c & d
end{pmatrix}
]$ $in Gamma_0(4) $, $(frac{c}{d})$ is the extended quadratic residue symbol and $c = b^2. $