Computer infected with malware? help!!!?

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Today I was browsing the web on google chrome and my computer started downloading some .exe file without my permission. I immediately cancelled the download so it wouldn't be completed. The file didn't get downloaded completely, so I guess I should be safe? I also didn't open anything, I cancelled it while it was downloading and deleted the unfinished file from my downloads-folder in google chrome.

I should be safe, right?
Even if it had downloaded completely, I had to execute it first before it would actually cause any harm, right?
Anyway, according to the download-folder in chrome it wasn't downloaded completely so there's no need to worry then.