The angular distribution of [Formula: see text] ([Formula: see text]) depends on two parameters, the lepton forward-backward asymmetry, [Formula: see text], and the flat term, [Formula: see text]. Both are strongly suppressed in the standard model and constitute sensitive probes of tensor and scalar contributions. We use the latest experimental results for [Formula: see text] in combination with the branching ratio of [Formula: see text] to derive the strongest model-independent bounds on tensor and scalar effective couplings to date. The measurement of [Formula: see text] provides a complementary constraint to that of the branching ratio of [Formula: see text] and allows us - for the first time - to constrain all complex-valued (pseudo-)scalar couplings and their chirality-flipped counterparts in one fit. Based on Bayesian fits of various scenarios, we find that our bounds even become tighter when vector couplings are allowed to deviate from the standard model and that specific combinations of angular observables in [Formula: see text] are still allowed to be up to two orders of magnitude larger than in the standard model, which would place them in the region of LHCb's sensitivity.