• $C[1,k]$ refers to the motive associated to $S_k(\Gamma_0(1))$
• $C^{-}[2,k]$ refers to the motive associated to the new part of $S^{-}_k(\Gamma_0(2))$
• $C^{+}[2,k]$ refers to the motive associated to the new part of $S^{+}_k(\Gamma_0(2))$
• $C[4,k]$ refers to the motive associated to the new part of $S_k(\Gamma_0(4))$