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 $c = b^2.$

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