The Patriots hired head coach Bill Belichick, who had served as defensive coordinator under Parcells including during Super Bowl XXXI, in 2000. Their new home field, Gillette Stadium, opened in 2002 to replace the aging Foxboro Stadium. Long–time starting quarterback Drew Bledsoe, who was the franchise's star throughout the 1990s, went down with a sheared blood vessel in his chest in a week two match–up in 2001 against the rival New York Jets. Backup quarterback Tom Brady, drafted by the Patriots in sixth round of the 2000 NFL draft, became the starting quarterback. Brady's successful play led to Bledsoe never getting his job back as a starter, and would serve as the franchise's starting quarterback for the next 18 years. Under Belichick and Brady, the Patriots became one of the most consistently dominant teams in the NFL, with many describing the team as a "dynasty". Within the first few seasons of the 21st century, the team won three Super Bowls in four seasons (2001, 2003, and 2004), over the St. Louis Rams, Carolina Panthers, and Philadelphia Eagles, respectively. The Patriots finished the 2007 regular season with a perfect 16–0 record, becoming only the fourth team in league history to go undefeated in the regular season, and the only one since the league expanded its regular season schedule to 16 games. After advancing to Super Bowl XLII, the team's fourth Super Bowl in seven years, the Patriots were upset by the Giants to end their bid for a 19–0 season. With the loss, the Patriots ended the year at 18–1, becoming only one of three teams to go 18–1 along with the 1984 San Francisco 49ers and the 1985 Chicago Bears. However, both the Bears and 49ers lost their only game during the regular season, and both would win their respective Super Bowl.

The Patriots returned to the Super Bowl in 2011 but lost again to the Giants, 21–17. In 2014, the Patriots reached a record-tying eighth Super Bowl, where they defeated the defending champion Seattle Seahawks by a score of 28–24 to win Super Bowl XLIX for their fourth title. After Seattle had driven the ball to New England's 1-yard line with under a minute to go, New England rookie cornerback Malcolm Butler made a critical interception on Seattle's final offensive play that helped to seal the victory. New England became the first team to reach nine Super Bowls in the 2016–17 playoffs and faced the Atlanta Falcons in Super Bowl LI. Losing 28–3 midway through the third quarter, the Patriots scored 25 unanswered points to tie the game in the final seconds of regulation. In the first overtime in Super Bowl history, the Patriots won the coin toss and scored a touchdown to claim their fifth Super Bowl victory. The Patriots extended their record to ten Super Bowl appearances in the 2017–18 playoffs but lost to the Philadelphia Eagles in Super Bowl LII. The Patriots returned to the championship game for a third consecutive season in Super Bowl LIII, where they defeated the Los Angeles Rams 13–3 to win their sixth Super Bowl, tying them with the Pittsburgh Steelers for most Super Bowl victories in NFL history.
Based on this passage, which years did the Patriots win the Super Bowl?
The Patriots won the Super Bowl in 2001, 2003, 2004, 2014, 2017, and 2019.