How can I fill in the deep v neck of my new sweater?
Not sure what you mean...is the V too deep? In that case, get a camisole with some pretty trim in a color you like with your sweater. The camisole should fit you well so it doesn't bag out where it shows in the V. Or if the V is not too deep, fill in the area with a multi-strand necklace.
Another option is a dickie. They can be casual or dressy and are found in numerous materials.
Here is a link that might be useful: Dickies-Google images