Rank-two Euler systems for symmetric squares

Let p\ge 7 be a prime number, and let f be a normalized eigen-newform with good reduction at p such that its pth Fourier coefficient vanishes. We construct a rank-two Euler system attached to the p-adic realization of the symmetric square motive of f. Furthermore, we show that the nontriviality is guaranteed by the nonvanishing of the leading term of the relevant L-value and the nonvanishing of a certain p-adic period modulo p.