Let f1, . . . , fd be an orthogonal basis for the space of cusp forms of even weight 2k on Γ0(N). Let L(fi, s) and L(fi, χ, s) denote the L-function of fi and its twist by a Dirichlet character χ, respectively. In this note, we obtain a “trace formula” for the values L(fi, χ,m)L(fi, n) at integers m and n with 0 < m, n < 2k and proper parity. In the case N = 1 or N = 2, the formula gives us a c...

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