In this section we give examples that illustrate how to use Theorem 5.4.2
to prove existence of elements of the Shafarevich-Tate group of a newform subvariety of
(for
and
) which are invisible at the base level, but become visible in a modular Jacobian of higher
level.
Hypothesis 6.0.1
The statements in this section all make the hypothesis that certain
commands of the computer algebra system Magma [BCP97] produce correct output.
(for 
and 
) which are invisible at the base level, but become visible in a modular Jacobian of higher
level.