# Restricting representations of the symmetric group to the cyclic group

Restrict an irreducible representation $$chi$$ of $$S_n$$ over $$mathbb C$$ to a representation of the cyclic group of order $$n$$, $$C_n$$. Is there a combinatorial expression for how $$chi$$ restricted to $$C_n$$ splits into irreducible representations of $$C_n$$?

I am able to compute this using the inner product on characters of $$C_n$$, but I wonder if there is another description using Young diagrams/partitions of $$n$$.