The geometry of higher weight modular symbols for
subgroups of SL_2(Z).
I will describe the definition of modular symbols, and
discuss in particular the case of certain weight 4 modular
symbols for congruence subgroups of genus zero.
I will describe how these correspond to 3 cycles in the fibre
product of the elliptic fibration over these varieties. In
some cases the variety is a rigid Calabi-Yau threefold, and I
will talk in particular about the case of Gamma_0(6).
Understanding the 3 cycles in terms of modular symbols
allows at least a numerical approximation to the intermediate
Jacobian, which is an elliptic curve in this case.
The material in this talk is well known to "the experts",
in abstract, but my intention is to give a down to earth,
concrete description, that one can actually compute with.