Yeah, vegan. As long as it doesn't come from an animal e. g milk and eggs, it should be fine. Though make sure to always check for additives that make contain animal products. Many foods will often state on the packaging whether or not they are suitable for vegans and/or vegetarians.
Unless there are traces of animal products either an actual part of an animal or something produced by them ( milk / eggs / yougurt...) , the food is vegan. Just check the packaging of the tomatoe paste to be safe.