This is the 2358th most frequent Russian word.
новыми
"New" (instrumental plural form).
The word 'новыми' is used here as an instrumental case, plural form of the adjective 'новый,' agreeing with the noun 'идеями' (ideas). It describes the quality of the ideas.
Мы обменялись новыми идеями.
We exchanged new ideas.
The adjective 'новыми' is in the instrumental case, plural form, matching the plural noun 'картинами' (paintings), describing these items being new.
Она украсила комнату новыми картинами.
She decorated the room with new paintings.
'Новыми' is used here in the dative case, plural form of the adjective 'новый', coupled with 'ученикам' (students) in the same case, to describe them as new.