Abstract Lie algebra

Question

For six dimensional Lie algebra with non-zero Lie brackets defined as follow: $[e_{1}, e_{3}] = -e_{1}, [e_{1}, e_{6}] = -e_{2}, [e_{2}, e_{3}] = -e_{2}, [e_{2}, e_{4}] = e_{1}, [e_{2}, e_{5}] = e_{2}, [e_{4}, e_{5}] = -e_{4}, [e_{4}, e_{6}] = -2*e_{5}-e_{3}, [e_{5}, e_{6}] = -e_{6}$. What would be quotient algebra $\frac{\text{Nor}\left(w_{1}\right)}{w_{1}}$ for $w_{1}=a*e_{3}+e_{5}$ ? Where 'a' is arbitrary constant $\neq 0, 1$ . The expected answer is $\{e_{3}\}$