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There's a karma threshold before you're allowed to downvote.

Could you tell me what that number is?

It goes up over time. Right now it's around 500.

For comments or posts?

Comments. I believe the threshold for flagging submissions is 1000, but I'm not sure; I didn't notice when I hit it. You cannot downvote submissions.

Flagging is considerably lower, this account can flag comments and submissions so I think ~20 karma is required to flag.