There are a lot of SQL Server settings that can affect performance outside of the server hardware specs. The indexes and statistics are restored as part of the database restore, so the fact that you just restored yesterday leads me to believe that is not the problem (at this point in time, but could become a problem in the future if not addressed). There are maintenance jobs that can rebuild indexes, also check your old server and see of there were any maintenance jobs that were setup that need moved to the new server. Compare the SQL Server configs between the two servers using
EXEC sp_configure 'Show Advanced Options', 1;
Note: The last sp_configure statement just shows configuration output and does not actually change any server config settings.
Also check the disk setups between the two servers, including the RAID types and disk speed. Make sure that your database and logs files are on separate disks which are also separate from your OS drive. Check the tempdb setups between the two servers as well. The recommendation to shrink the database in one of the answers is not advised, as this can lead to fragmentation in the database. If there is any auditing software or anti-virus that is on the new server but not on the old server than this could cause issues. Make sure the new server has recent OS patches applied and compare the SQL Server service pack levels between the two servers.