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Given a pair of modular forms with complex multiplication by distinctimaginary quadratic fields, the four dimensional Galois representationassociated to their Rankin--Selberg convolution is induced from a characterover an imaginary biquadratic field $F$. Using the Euler system of Lei,Loeffler and Zerbes we bound a Selmer group associated to this character, overthe unique $\mathbb{Z}_{p}^{3}$-extension of $F$.

An Euler system for characters over an imaginary biquadratic field