We revisit the construction of the renormalized trace Θ of the Energy-Momentum tensor in the four-dimensional $\lambda {\varphi }^4$ theory, using dimensional regularization in $d=4-\epsilon$ dimensions. We first construct several basic correlators such as $\langle {\varphi }^2\varphi \varphi \rangle$, $\langle {\varphi }^4\varphi \varphi \rangle$ to order ${\lambda }^2$ and from these the correlators $\langle K_I\varphi \varphi \rangle$ and $\langle K_I{K}_J\rangle$ with $K_I$ the basis of dimension d operators. We then match the limit of their expressions on the Wilson-Fisher fixed point to the corresponding expressions obtained in Conformal Field Theory. Then, using the 3-point function $\langle \Theta \varphi \varphi \rangle$, we construct the operator Θ as a certain linear combination of the basis operators, using the requirements that Θ should vanish on the fixed point and that it should have zero anomalous dimension. Finally, we compute the 2-point function $\langle \Theta \Theta \rangle$ and we show that it obeys an eigenvalue equation that gives additional information about the internal structure of the Energy-Momentum tensor operator to what is already contained in its Callan-Symanzik equation.