Manufactured in 1913; model should be a Flues or NIG (New Ithaca Gun), as either could have had that serial number. Value depends on condition and how badly someone wants to buy it. 12 GA is more common than 16 or 20, so is worth less. Ballpark is probably in the $350 range. Watch gunbroker.com for a little while and see what similar guns are bringing at auction.
1906
The serial number indicates Ithaca manufactured your Model 37 in 1956.
Date of Mfg. is 1947
1949
you might be able to get a answer at arms collectors.com
I thought that would be in the end of the serial range of Ithaca but 1944.
http://www.diamondgunsmithing.com/page5/page23/index.html
There's a list of serial numbers by year at http://ithacagunrepair.com/page5/page23/
There's a list of serial numbers by year at http://ithacagunrepair.com/page5/page23/
depends on the year and manufacture date of your gun . also do all the parts match by serial Number you should find the serial Number on side of the receiver (on newer Ithaca) older style Ithaca the serial Number will be on the Recevier (Between the magazine tube and barrel) then look up WWW.SURPLUSRIFLEFORUM.COM on their site look up on their Search engine type in "ITHACA 37 DOM" there you'll find the serial list number
Ithaca made 382,000 of these between 1942 and 1945, but I don't know of a source for narrowing it down farther than that. Not sure about the serial number, as Ithaca was assigned serial numbers of 7 digits, beginning with 1,208,674 and ending with 2,693,613, but not sequential. Ithaca was awarded the only "E" for excellence in manufacture of these pistols of the 3 companies that made them for the military.
The Lefever Nitro Special was made by Ithaca. Yours was made in 1923.