wow, people need to read the first post before they reply.
vibebreaker - it would either over rev the engine or just not shift at all and slow the engine down before actually shifting down. depends how the auto tranny is set up.
tigrpal - the rpms are always exactly the same at a certian engine speed, it's a gearing issue, the wheels spin at a certain ratio to the speed the engine is spinning determined by what gear you're in. it doesn't matter if you're going uphill or downhill
EDIT: on automatics this isn't the case, but he has a manual.
sureshot324 - wish I could help you, I know exactly why you would want to know this. but I don't have a 01 corolla :-P. I hope someone lets you know. you're probably aren't over revving it though, just shift when you feel the power start to drop off. a lot of times redline isn't the best place to shift anyway. I would recommend getting a stock corolla gauge cluster with a tach though, big aftermarket ones are hidious. sorry I can't help.