Hi Welcome to the Forum.
You say "new". Do you mean new to you ? as your profile states the car is a 2011 model. If this is the case you are now out of warranty and you can take your car anywhere you like to get any work done.
Including any other Mazda dealer
There are pro and cons regarding Mazda dealerships. The pros are, the technicians have familiarity with the car and instant access to any parts required (subject to availability) And the ability to update your electronic servicing schedule.
The cons are that the recognised franchised dealerships are usually more expensive than an independent garage.
Most independents will offer to use genuine Mazda parts, but some will not have the necessary equipment to update the aforesaid servicing schedule.
You pays your money you take your choice.