We explicitly write down the Eisenstein elements inside the space of modular symbols
for Eisenstein series with integer coefficients for the congruence subgroups
with
and
distinct odd primes, giving an answer to a question of Merel in these cases. We also
compute the winding elements explicitly for these congruence subgroups. Our results
are explicit versions of the Manin–Drinfeld theorem.
Keywords
Eisenstein series, modular symbols, special values of
$L$-functions