Q:

How to horizontally align elements of lists

I would like the elements of a tuple of two lists to have the same horizontal alignment. I have tried the following:
\documentclass{report}
\usepackage{amsmath}

\begin{document}
\[
  C_0 = \left(
  \begin{aligned}
    (&f_1, &f_2, &f_3, &f_4), \\
    (&0, &0, &1, &0)
  \end{aligned}
  \right)
\]
\end{document}

This results in:

I have tried replacing the aligned environment with a matrix environment, but this results in too much spacing between elements of the list:

A:

Is it something like this you want?
\documentclass{article}
\usepackage{amsmath}

\begin{document}

\[ \setlength\arraycolsep{1pt}
  C_0 = \begin{pmatrix}
    ( f_1, &f_2, &f_3, &f_4 ), \\
    ( 0, &0, &1, &0 )
  \end{pmatrix} \]
\end{document} 

