Note that the password is for your entire Spectrum account, not just to access the Forums. To change it after you have logged in, you first need to sign out. Then just click the "Sign In" button again, select 'Forgot Password?' and Spectrum will step you through the process of creating a new one.
In addition, you can also manage your password by logging into your Spectrum My Account at spectrum.net and going to the My Profile tab, then select Edit for the Password field.
Keep in mind that the Forums and My Account passwords are the same. As well, this will also change the password for Spectrum TV and any Channel apps you might use.