Newby question about stem directions

[Tim Rowe]

I can't get the following bit of notation to work -- despite the
\stemUp command the stems are down (which looks horrid!) -- can
anybody tell me what I'm doing wrong? Thanks.:

\version "2.12.2"
\include "english.ly"

lower = \relative c {
  \clef bass
  \key f \major
  \time 4/4

  <<  {\stemDown c2 } {\stemUp e4 e4 } \stemNeutral >> c2 |
}

\score {
  <<
  \set Score.tempoHideNote = ##t
  \tempo 4 = 144
    \new PianoStaff <<
      \new Staff = "lower" \lower
      >>
  >>
  \layout {
    \context { \RemoveEmptyStaffContext }
  }
  \midi { }
}

-- 
Tim Rowe