On a parity result for the symmetric square of modular forms with congruent residual representations

The parity of Selmer ranks for elliptic curves defined over the rational numbers $\mathbb{Q}$ with good ordinary reduction at an odd prime $p$ has been studied by Shekhar. The proof of Shekhar relies on proving a parity result for the $λ$-invariants of Selmer groups over the cyclotomic $\mathbb{Z}_p