Let $p\ge 5$, and let $(a,b,c)\in\mathbb Z^3$ be a primitive Fermat solution, meaning $abc\neq 0$, $\gcd(a,b,c)=1$, and $a^p+b^p+c^p=0$. Choose the standard Frey normalization, after permuting and changing signs if necessary, in which $b$ is even and $a\equiv -1 \pmod 4$, and set $E_{a,b,p}: y^2=x(x-a^p)(x+b^p)$. If the semisimplified residual representation $\bar{\rho}_{E_{a,b,p},p}$ is modular and absolutely irreducible, then there exist a normalized weight $2$ newform $f\in S_2(\Gamma_0(2))$ and a prime $\mathfrak p$ of the coefficient field of $f$ above $p$ such that $\bar{\rho}_{E_{a,b,p},p}\cong\bar{\rho}_{f,\mathfrak p}$.