Mazur–Rubin's variance asymptotic conjecture for modular symbols

Let $f\in S_2(\Gamma_0(q))$, where $q$ is a positive integer. For each positive integer $c$, define

$$\operatorname{Var}(f,c)=\frac{1}{\phi(c)}\sum_{\substack{a\bmod c\\(a,c)=1}}\left(\langle a/c\rangle-\operatorname{E}(f,c)\right)^2,$$

where $\langle r\rangle=\int_{i\infty}^r\operatorname{Re}(f(z)\,dz)$ and $\operatorname{E}(f,c)$ is the corresponding mean. Mazur–Rubin's variance asymptotic conjecture. There exists a constant $C_f$ and, for each divisor $d$ of $q$, a constant $D_{f,d}$ such that

$$\lim_{\substack{c\to\infty\\(c,q)=d}}\left(\operatorname{Var}(f,c)-C_f\log c\right)=D_{f,d}.$$

The constant $C_f$ is the variance slope and $D_{f,d}$ is the variance shift. The conjecture predicts the asymptotic growth of the second moment of modular symbols along each fixed gcd class with the level; the supplied text gives no resolution status.