Unity does not parse code properly.

I have a script 'fa' attached to an empty object. It contains the following:

using System.Collections; using System.Collections.Generic; using UnityEngine;

 public class fa : MonoBehaviour
 {
     // Start is called before the first frame update
     void Start()
     {
         public List<Vector2> housePositions = new List<Vector2>();
     }
 }

I am then presented with the following errors: Assets\fa.cs(14,1): error CS1022: Type or namespace definition, or end-of-file expected Assets\fa.cs(14,2): error CS1022: Type or namespace definition, or end-of-file expected Assets\fa.cs(9,6): error CS1513: } expected

Unless there is something obvious which I am completely missing, I am fairly sure that Unity just isn't parsing the code properly. I have tried uninstalling Unity and Unity Hub, deleting VS Tools 2015, deleting my project and reimporting it, installing other Unity versions. Pretty much everything I could think of, bar reinstalling windows. Is there something else that could potentially solve this?