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

Let f be a normalized newform of weight 2 on Γ₀(N) whose coefficients lie in Q and let χM be a primitive quadratic Dirichlet character with conductor M. In this paper, under mild assumptions on M, we give a sharp lower bound of the 2-adic valuation of the algebraic central L-value L(f, χM, 1) and evaluate the 2-adic valuation for an infinite number of M.