Example 1
Let
f = q + (−i − 1)q2
+ (i − 1)q3
+ O(q4
) ∈ S2 Γ1(16)


and
l = (5, i − 2).
We catch ρf ,l in the 5-torsion of the Jacobian of X1(16)
(genus 2).
S = mfinit([16,2,0],1);
f = mfeigenbasis(S[1])[1];
R = mfgalrep(f,[5,[[2,2]]],[30,50],5)
factor(projgalrep(R)[1])
Nicolas Mascot p-adic computation of Galois representations