If you are not going to update the content very often, I would recommend to use subdirectory instead of subdomain because it will keep the SEO value consolidated under the main domain.
It will also ensure that any existing SEO authority of your main domain benefits the content and reduces the effort required for visibility in search results. Usually, stale subdomains struggle to rank well without frequent updates.
But if you feel that in future your forum will have large number of members and frequent updates, you can go with subdomain. However, even in such case, use of subdirectory will not hurt SEO.