This is the 8513th most frequent Russian word.
новогоднeго
"Новогоднего" means "of the New Year" in English.
The word 'новогоднего' is used as an adjective in the genitive case to describe 'праздника', indicating the possession or relationship of the celebration to the New Year.
Я купил подарки для новогоднего праздника.
I bought gifts for the New Year's celebration.
In this context, 'новогоднего' acts as an adjective in the genitive case describing 'дерева', signifying the New Year's association of the tree.
В детстве я всегда любил запах новогоднего дерева.
In childhood, I always loved the smell of the New Year's tree.
Here, 'новогоднего' is used as an adjective in the genitive case modifying 'настроения', reflecting the thematic mood tied to New Year.