The 501 is the serial number. According to the old Remington Arms Co., Inc. factory ledger, the Model 31 receiver with serial number 501 was put in work between 5 and 10 July 1931. Here is a Model 31 ad from the June 1931 issue of
Field & Stream --

- Model 31 ad June 1931 Field & Stream.jpg (115.12 KiB) Viewed 3424 times
and an early Model 31 brochure --

- Model 31 3-shot Brochur.jpg (151.93 KiB) Viewed 3424 times
Looks like a nice early example. The Model 31A "Standard" Grade wood was checkered from the Model 31 introduction until 1937 when the Model 31AP "Standard" Grade was introduced with a plain stock and the ringed forearm --

- Model 31AP Standard Grade.jpeg (321.8 KiB) Viewed 3424 times
For 1937 and 8 they sold off the old checkered "Standard" Grades as the Model 31AC "Standard" Grade --

- Model 31AC Standard Grade 8-37.jpeg (508.33 KiB) Viewed 3424 times
By 1939 there was just the Model 31A "Standard" Grade, now with the plain stock and ringed forearm.
If the stock is full length to the original butt plate, and the barrel is the most common 30-inch full choke, it would max out at $300 in the pawn shops around here. If the stock has been cut and a recoil pad installed that would drop the price. Probably a bit of a premium for a 28-inch modified choke barrel and a bit more for a 26-inch improved cylinder or the 32-inch full choke barrel.