Pilot reported accidentally taxiing onto an unmarked service road on a large paved area at SYR after mistaking it for a taxiway.

Narrative

I received my IFR clearance and just obtained my taxi instructions from SYR Ground to taxi to Runway 15 via A - B - M from the FBO. I had already done a runup in the very large asphalt space just to the southwest of the aircraft parking; but still on the ramp. Upon read back of the taxi clearance; I proceeded straight ahead to what I though was to lead to Taxiway A. Once on the roadway; I realized things were not right. At that point; I received a call from Ground telling me I was on a service road. The service road was not on the FAA airport [diagram]; and I saw no signs indicating it was a service road where I entered it. I requested directions from Ground to get to Taxiway A and the ground controller was very helpful in getting onto Taxiway A headed to Taxiway B. Being on the eastern side of the large; paved area extension of the FBO; I did not see the exit to Taxiway A on the far right of my position and saw no signs indicating the way was a service road. Looking at the airport chart; I should have realized that Taxiway A started at the SW edge of the large; paved area departing the FBO. I was thinking that the roadway I took would lead to taxiway A. My mistake.