The automorphism group of any Riemann surface of genus greater than 1 is a finite group. From each linear representation of this group, a fibration of Riemann surfaces (with singular fiber) is obtained (``linear quotient family''). Typical representations of an automorphism group are the homological representation and the canonical representation; the latter is the representation on the space of holomorphic quadratic differentials, and the linear quotient family obtained from this representation linearly approximates the universal family of Riemann surfaces around the surface. In this talk, for the Klein curve (the Riemann surface of genus 3 with the largest automorphism group $PSL_2 (\mathbb{F}_7)$), we describe the linear quotient families obtained from the homological and canonical representations, and describe the universal family around the Klein curve.