Here's an update on this issue. I took it to a dealership three months ago. They said they could not find anything wrong with it and that they could not reproduce the problem. But, when I drove it home, I noticed that it was not shaking as bad as before. For about two months the shaking at the stop light has been very faint. I think they did something to it and it worked for a while. I do not know what though...
In the past month it has been getting gradually worst to the point where in the last couple of days it's been very bad. The car shakes pretty strong. It's almost like the idle is too low and it's going to stall and the computer compensates by revving it up just a bit. I'll take it to the dealership again to see what they say.
{UPDATE}
I got the car back from the Chevrolet dealership/ service center yesterday. I had four issues with it:
1) Shaking while idle
They did nothing on this. They said they could not reproduce the problem so they left it at that. This was the second time I took the car in for that problem.
Looking on carcomplaints(dot)com I found a Technical Service Bulletin for 2013 Sonics that describes the problem I’m having. I was expecting the service center to do at least that TSB to remedy the problem. Here’s the TSB:
TSB #PI0928
NHTSA ID #10052020
Date Announced:
MARCH 01 2013
Summary: GM: SOME CUSTOMERS MAY REPORT A BUMP, SURGE OR VIBRATION AT IDLE WITH THEIR FOOT ON THE BRAKE. *JS
2) Grinding noise from rear of the car when braking. They said they did nothing on it. I cannot hear it as loud as before I took the car in. So they DID something, probably not the right thing though. Also looking on the site I mentioned before, I found a Technical Service Bulletin that describes the problem. Here it is:
TSB #PIC-5781-A
NHTSA ID #10054212
Date Announced:
NOVEMBER 01 2013
Summary: CHEVROLET: ROTATIONAL NOISE COMING FROM REAR OF VEHICLE WHEN BRAKING, IN REAR DRUM BRAKE AREA AND NEED TO REPLACE BOTH REAR BRAKE DRUM AND SHOES ON BOTH SIDES. MODEL 2012-2013 SONIC. *PE
3) High pitch noise (chirping sound) from air blower fan/motor. This happens infrequently, when I have the air on speed 1 and 2. It is very annoying when it happens; I can’t stand the noise so I have to either crank up the speed or turn it off completely. I made sure that the service clerk put notes about this in the service request. The Service guys did nothing on this issues. They said they could not reproduce it and left it at that.
4) Lost one of the two little plastic brackets holding the plastic interior trunk lid to the pivots sticking out from the sides of the car. I wanted to buy it. Apparently they do not sell just that part. I have to buy the whole trunk lid.
So, in conclusion, I am very disappointed by the Chevrolet service. I suspect they will drag this on until my warranty expires (it has 25k miles on it so far) and then they will tell me “Oh yeah, we know about those issues. We even have TSBs on them. It will be $X,000 to fix them.”
I bought this car with high hopes. Seems to be a very nice car until you run into problems like these. Shame...