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Given a modular formf{{f}}    of even weight larger than two and an imaginary quadratic fieldK{{K}}    satisfying a relaxed Heegner hypothesis, we construct a collection of CM cycles on a Kuga–Sato variety over a suitable Shimura curve which gives rise to a system of Galois cohomology classes attached tof{{f}}    enjoying the compatibility properties of an Euler system. Then we use Kolyvagin’s method [ 21 ], as adapted by Nekovář [ 28 ] to higher weight modular forms, to bound the size of the relevant Selmer group associated tof{{f}}    andK{{K}}    and prove the finiteness of the (primary part) of the Shafarevich–Tate group, provided that a suitable cohomology class does not vanish.

CM cycles on Kuga–Sato varieties over Shimura curves and Selmer groups