A speeding ticket for going between 31 and 40 mph over the speed limit is an 8 point offense in New York State as you stated.
In 1999, the NY governor signed into law a bill allowing drivers cited for going more than 30 mph above the speed limit in a school zone to have imposed on them a fine of not less than $240 nor more than $800, or a penalty of not more than 30 days imprisonment, or both.
If you receive 11 points or more in 18 months the NY DMV suspends your driver's license. So you will want to drive safely and not receive any more point violations on your record for the next 18 months so that you do not get 11 or more points in total on your license.
Insurance companies have points systems different from the DMV driver violation points system; each company in fact can have their own rating system. So to find out how your rates may be affected by this violation you will have to contact your insurance company.
To help with your points total and insurance rates you might want to take a DMV approved accident prevention course. Under the Point and Insurance Reduction Program (PIRP) and you can reduce your driver points by 4 and save 10 percent on your liability and collision insurance. The NY DMV site of www.nydmv.state.ny.us/broch/c32a.htm gives information on how this program works.