Aperture in Program Mode on SLT-A37

I am using the SLT-A37 with 18-55mm kit lens. I noticed that in Program mode it keeps the aperture down to f/4.0 even at the widest when the maximum possible is f/3.5 even when the light is low, until the ISO reaches 3200. I would like to use the Sony 35mm f/1.8 lens but I am wondering if it will do the same with that lens too: i.e., keep it stopped down to f/4.0, thereby negating any advantage of the faster lens. Unfortunately, Sony does not publish their program lines in the manual. Does anyone have experience with this combination and knows what the behavior is in low light? Any information you can provide will be helpful. Thanks.