William Moulton (WM on the coin) was empowered by the newly formed House of Representatives to make a copper coin in 1776. Not much more is known about these coins. They did not appear in circulation. If you should have a genuine New Hampshire copper, it is essentially priceless, worth 100s of 1000s of dollars.
However, it is essentially impossible to find such a coin. In China, and other emerging free-market countries, counterfeiters are enjoying their regulation-free atmosphere and flooding the market with fake rare coins. That is, in all probability, what you have. It is worth a few US dollars as a novelty, even if it does not carry the COPY inscription which is mandated in the US, but not in many other countries.
A note in this CoinTalk thread refers to famous coin cataloger Walter Breen and how he says a genuine piece has a weight of 79.5 grains, or 5.15 grams. If your coin weighs that much, submit it to PCGS, NGC, ANACS, or ICG for authentication. Look these up on the Internet. Do not use other services.
Coin buying has always been a Buyer Beware proposition. In today's economic climate, it is even more so. For more looks at counterfeit coins, visit this CoinQuest collection of them.