alszik "to sleep" and álom "dream" are related if you go back far enough, as I found out just now. (Perhaps that will help someone remember the two.)
That is interesting, thanks! Yeah, actually, "sleepy" is "álmos" in Hungarian. It does not match "dreamy". "Dreamy" would be more like "álmodozó".
Is alszom the indefinite conjugation? If so then why? because "a" is definite...
verbs ending in -ik (alszik, eszik, iszik...) are exeptions, they have an -m ending in first person indefinite conjugation too.