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