There's a slight misunderstanding in the question. All chromosomes carry traits, even sex chromosomes. They just carry different sets of traits compared to non-sex chromosomes (autosomes).

Here's a breakdown:

* Sex chromosomes: These determine an individual's biological sex. In humans, these are X and Y chromosomes.

* Autosomes: These are all the other chromosomes besides the sex chromosomes.

* Traits: These are characteristics or features that are passed down from parents to offspring. Every chromosome carries genes, which contain the instructions for these traits.

So, while it's true that the Y chromosome is much smaller than the X chromosome and carries fewer genes, both X and Y chromosomes still carry important traits. For example, the Y chromosome carries genes for male sex development, and the X chromosome carries genes for a variety of traits unrelated to sex.

Therefore, there aren't any sex chromosomes that don't carry traits. It's more accurate to say that different sex chromosomes carry different sets of traits.