  For every point on the Jacobian of the modular curve $X_0(l)$ we define and
study certain twisted holomorphic Eisenstein series. These are particular cases
of a more general notion of twisted modular forms which correspond to sections
on the modular curve $X_1(l)$ of the degree zero twists of line bundles of
usual modular forms. We conjecture that a point on the Jacobian is rational if
and only if the ratios of these twisted Eisenstein series of the same weights
have rational coefficients.
