Euler Systems for ${\mathrm{G}\mathrm{S}\mathrm{p}}_4\times {\mathrm{G}\mathrm{L}}_2$

For a non-endoscopic cohomological cuspidal automorphic representation of ${\mathrm{G}\mathrm{S}\mathrm{p}}_4\times {\mathrm{G}\mathrm{L}}_2$, assumed to be $p$-ordinary, we construct an Euler system for the Galois representation associated to it. Both the construction and the verification of tame norm relations are based on Novodvorsky’s integral formula for the $L$-function of $$\mathrm{G}\mathrm{S}\mathrm{p}$_4 \times $\mathrm{G}\mathrm{L}$_2$.