What type is this switch?
Take the switch you bought back and get a 3-way

That switch is a 3-way switch (the term "common" as part of the labeling for the terminals is a dead giveaway).  Unfortunately, using a four-way as a three-way will probably confuse the next person to work on it, so it's better to take it back and just get a 3-way instead (it'll also get you some of your hard-earned money back as a return credit).

P.S. when you wire the new switch, use the side-screws not the back-stabs. It'll save you a bunch of trouble in the long run.