  We show how one can use the representation theory of ternary quartics to
construct all vector-valued Siegel modular forms and Teichm\"uller modular
forms of degree 3. The relation between the order of vanishing of a concomitant
on the locus of double conics and the order of vanishing of the corresponding
modular form on the hyperelliptic locus plays an important role. We also
determine the connection between Teichm\"uller cusp forms on \overline{M}_g and
the middle cohomology of symplectic local systems on M_g. In genus 3, we make
this explicit in a large number of cases.
