# Atkin-Lehner + Galois adapted basis of S_2(Gamma_0(143)).
# e_k = sum_i B[i][k] f_i, with f_i the PARI mfbasis.
# W_11 and W_13 are SIMULTANEOUSLY DIAGONAL in this basis:
#   W11 diag = [1]*7 + [-1]*6 ;  W13 diag = [1,-1*6,1*5,-1]
# Coordinate labels (block, sector):
#   y1   f1    (+,+)
#   y2   f3    (+,-)
#   y3   f3    (+,-)
#   y4   f3    (+,-)
#   y5   f3    (+,-)
#   y6   f3    (+,-)
#   y7   f3    (+,-)
#   y8   old+  (-,+)
#   y9   f2    (-,+)
#   y10  f2    (-,+)
#   y11  f2    (-,+)
#   y12  f2    (-,+)
#   y13  old-  (-,-)
# det B = -1078272
#
i,e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13
f1,0,0,0,0,0,0,0,1,0,0,0,0,1
f2,0,0,0,0,0,0,0,13,0,0,0,0,-13
f3,20,0,0,0,-2,1,-1,0,1,0,4,-3,0
f4,0,-4,0,0,0,-4,0,0,0,0,0,0,0
f5,-8,-1,0,-1,-1,-1,-2,0,0,0,2,2,0
f6,-10,1,0,0,-1,1,0,0,0,2,1,-1,0
f7,-9,0,1,-1,-1,-1,-2,0,0,1,0,-2,0
f8,-7,0,0,-1,-1,1,0,0,0,2,1,-2,0
f9,-5,-2,1,0,-1,-1,0,0,0,-1,-1,1,0
f10,-3,1,0,-1,0,0,0,0,0,0,0,1,0
f11,-2,0,-1,0,0,0,0,0,0,-1,-1,0,0
f12,-1,0,0,0,0,0,1,0,0,0,1,0,0
f13,-1,3,-1,2,4,3,3,0,1,-1,4,-3,0
