Laravel Eloquent with `has` and `where` on dates

I try to get records on relation when there is only one record in the one to many relation and only the records where the start_date is bigger than now() and here is what I'm trying:

$newStarters = User::has('periods', 1)->with(['periods' => function($q) {
            $q->where('start_date', '>', Carbon::now()->subWeek(2)->format('Y-m-d') );
        }])->get();

in this case the date filter does not applies.

What is the propper way to do this?

via Chebli Mohamed