I'm trying to redo some of the computations being done in Section 6 of
http://math.bu.edu/people/rpollack/Papers/Overconvergent_modular_symbols.pdf
May I ask how is $\varphi_f(D_1)=\frac{1}{5}, \varphi_f(D_2)=\frac{-3}{2}, \varphi_f(D_3)=\frac{1}{2}$ being obtained?
I apologise if I should be asking this question on stackexchange instead of here. I wasn't sure which was the better place for a seemingly trivial question like this, even though it is from a research paper.
I remember once asking Rob Pollack, at a conference in Oxford, what the running time of his algorithm to compute overconvergent modular symbols was. His response was, "We have an algorithm?". He subsequently explained to me that their algorithms do not compute overconvergent modular symbols "ab initio"; they require as input the values of a classical modular symbol (and the algorithms then produce a lifting of this to an overconvergent symbol).
The way to find this classical symbol is explained in section 2 of their paper, in particular the last few lines of section 2.10; it's a well-established theory, going back to work of Birch and Manin in the 1960s. Modulo minor differences of conventions, it's the same algorithm that is explained in great detail in William Stein's book Modular Forms: A Computational Approach.
