# Bound 1-norm of Chebyshev coefficients in terms of supremum norm of function

Is there a constant $$C$$ such that $$\|c_k\|_{1} \leq C \, \|f\|_\infty$$ with $$c_k$$ the Chebyshev coefficients of $$f$$?

I'm assuming the answer is no, but I can't find a counterexample.