The Teitelbaum conjecture in the indefinite setting

Let f be a new cusp form on Gamma_0(N) of even weight k+2>=2. Suppose that there is a prime p dividing N and that we may write N=pN^{+}N^{-}, where N^{-} is the squarefree product of an even number of primes. There is a Darmon style L-invariant L_N^{-}(f) attached to this factorization, which is the Orton L-invariant when N^{-}=1. We prove that L_N^{-}(f) does not depend on the chosen factorization of N and it is equal to the other known L-invariants. We also give a formula for the computation of the logarithmic p-adic Abel-Jacobi image of the Darmon cycles. This formula is crucial for the computations of the derivatives of the p-adic L-functions of the weight variable attached to a real quadratic field K/Q such that the primes dividing N^{+} are split and the primes dividing pN^{-} are inert.