Yes, certain types of spells are more effective or powerful during the new moon or full moon than at other waxing or waning phases of the moon.
Heres some notes i took a while back:
A waxing or full moon is best for spells that are adding something. Summoning, bringing forth energy, attracting wealth or love, enchanting something etc.
A waning or new moon is best for spells that remove something. Banishing, dispelling a curse, removing unwanted energy and emotion, etc.
Let the dark moon be an end to old projects and worries in pursuit of new ones. Perform a cleansing or peaceful ritual to rid all worries.
I do this almost every new moon. And it helps me relax before bed even on other nights that arent the new moon. And i dont really do anything too complex, but you can if you want. C: