Quadratic modular symbols

We study a special kind of homology cycles of the modular curve X0(N). For a newform of weight 2 for Γ0(N), we construct a p-adic L-function by using these cycles. If the newform is defined over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Q}}$$\end{document}, this p-adic L-function gives rise to algebraic points of the attached elliptic curve.