The 2-adic valuations of the algebraic central $L$-values for quadratic twists of weight 2 newforms

Taiga Adachi, Keiichiro Nomoto, Ryota Shii

Let $f$ be a normalized newform of weight 2 on $\hat{I}{“}_0(N)$ whose coefficients lie in $\mathbb{Q}$ and let $\ddot{I}{‡}_M$ be a primitive quadratic Dirichlet character with conductor $M$. In t…