You will need to have SA level account / or DBcreater account on SQL in order to create new Database. see below full details.
In most installations of SQL Server "sa" account is disabled. Question is - did your DBA did it on purpose, or maybe you installed SQL Server yourself and not enabled "sa" account. Nevertheless you will need to enable this account or use any other account as my colleague mentioned above.
You may find these posts useful (especially first one)