How do I use "should" to describe the past tense? Eg, you should be in the same class with me last quarter. But all the tense is present tense

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you should have been in the same class with me last quarter.

you should've been in the same class with me last quarter.

The phrase should have indicates a missed obligation or opportunity in the past. In informal speech, it is contracted to should've.
I should have (should've) known you were lying. Tom and Pauline are so selfish, they should have (should've) been there for you.