We will introduce a large class of $\mathcal{N}=1$ superconformal theories, called

$S_k$, which is obtained from Gaiotto's $\mathcal{N}=2$ class $S$ via orbifolding. We

will study the Coulomb branch of the theories in the class by

constructing and analyzing their spectral curves. Using our experience

from the $\mathcal{N}=2$ \textsc{agt} correspondence we will search for a 2d/4d relations

(\textsc{agt}${}_{k}$) for the $\mathcal{N}=1$ theories of class $S_k$. From the curves we will

identify the 2d \textsc{cft} symmetry algebra and its representations, namely

the conformal blocks of the Virasoro/W-algebra, that underlie the 2d

theory and reproduce the Seiberg-Witten curves of the $\mathcal{N} = 1$ gauge

theories. We find that the blocks corresponding to the ${\rm SU}(N)$ $S_k$ gauge

theories involve fields in certain non-unitary representations of the

$W_{k,N}$ algebra. These conformal blocks give a prediction for the

instanton partition functions of the 4d $\mathcal{N} = 1$ \textsc{scft}s of class $S_k$.

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