Let \( \{ \varphi_0, \varphi_1, \varphi_2, \dots \} \) be an orthonormal set in \( L^2[-1, 1] \) such that \( \varphi_n = C_n P_n \), where \( C_n \) is a constant and \( P_n \) is the Legendre polynomial of degree \( n \), for each \( n \in \mathbb{N} \setminus \{0\} \). Then, which of the following statements are TRUE?