Mean squares of quadratic twists of the Fourier coefficients of modular forms

In this paper, we evaluate asymptotically a smoothed version of the sum $${\displaystyle \text{sideset}{}^{\ast }\sum _{d\le X}{(\sum _{n\le Y}{\lambda }_f(n)(\frac{8d}{n}\left)\right)}^2,}$$ where $\left(\frac{8d}{\cdot }\right)$ is the Kronecker symbol, $\text{sideset}{}^{\ast }\sum$ denotes a sum over positive odd square-free integers and ${\lambda }_f(n)$ are Fourier coefficients of a given modular form $f$.