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I know trotz should be used with genitive, e.g:

Trotz des Regens gehe ich zur Schule.

But, I don't understand the case in the example below. It is not dative for plural, as Freunde not Freunden. Also not genitive for plural, der neuen not des neuen.

Trotz der neuen Freunde hat sie oft Heimweh.

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In spite of the new friends, she is often homesick.

Now, as far the genitive is concerned, you could have, for example:

Das Messer des Mannes - The knife of the man.
Der Wagen der Frau - The car of the woman.
Der Zahn des Kindes - The tooth of the child.

Or, in the plural:

Das Messer der Männer - The knife of the men.
Der Wagen der Frauen - The car of the women.
Der Zahn der Kinder - The tooth of the children.

Here are some examples with trotz:

Trotz des Wetters fahren wir heute nach Hause - In spite of the weather, we're driving home today.
Trotz meines Versuchs - Despite my attempt.
... trotz zahlreicher Proteste - ... notwithstanding numerous protests. Trotz intensiver Suche - Despite an intensive search.
Trotz aller Bemühungen - Despite all efforts.

In summary:
Trotz + des... means that what follows is a masculine or neuter noun in the singular.
Trotz + der... could indicate either a feminine noun in the singular, or anything in the plural.

TL;DR: take a look at the following table https://deutsch.lingolia.com/en/grammar/declension/genitive

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  • It's das Messer here
    – Arsak
    Sep 5 '20 at 0:34

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