I mean the most important space on your website. In this case, the header, the part of the website before the reader has to scroll down the page. In some cases that is the only thing your new website visitor will see when they visit your website.
You don't have that much time to get their attention.
You want to give them a reason to stay.
Or entice them to dig in.
That would be the job of the Headline. Which in this case could stand to be much larger.