for the manual to this tractor.
There may be a few problems with your unit.
1. Bad battery (but you said it's new)
2. Bad regulator
3. Bad alternator (aka stator in this type of engine).Page 33
of the manual has the electrical schematic.
This tractor is not equipped with a regulator.
You will find in the schematic that the battery charging diode sends power through the ignition switch path to charge the battery.
Check for voltage (3A DC) before and after the diode to verify correct power.
Then you will need to check it on it's path from the ignition switch to the battery (usually at the fuse is fine)
The most common place for failure is the starter solenoid wiring being corroded or broken. however absence of proper voltage points to the stator.
#10 on page 52 of the manual is the stator (part # XXXXX referenced on pg 53)CLICK HERE
to see/order the part for approx $43.
Since you indicate 0 voltage at the battery - it's almost certain the stator is to blame.
Thanks for using J.A.