{{{id=1|
time M = ModularSymbols(Gamma1(29))
///
Time: CPU 0.73 s, Wall: 0.75 s
}}}

{{{id=2|
M
///
Modular Symbols space of dimension 71 for Gamma_1(29) of weight 2 with sign 0 and over Rational Field
}}}

{{{id=3|
S = M.cuspidal_submodule()
///
}}}

{{{id=4|
S
///
Modular Symbols subspace of dimension 44 of Modular Symbols space of dimension 71 for Gamma_1(29) of weight 2 with sign 0 and over Rational Field
}}}

{{{id=5|
time I = M.integral_structure()
///
Time: CPU 0.05 s, Wall: 0.13 s
}}}

{{{id=6|
I.basis_matrix().det()
///
1
}}}

{{{id=7|
I.basis_matrix() == 1
///
True
}}}

{{{id=8|
time db3 = S.diamond_bracket_operator(3).matrix()
///
Time: CPU 0.28 s, Wall: 0.28 s
}}}

{{{id=9|
db3.fcp()
///
(x - 1)^5 * (x + 1)^6 * (x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)^4 * (x^6 - x^5 + x^4 - x^3 + x^2 - x + 1)^6
}}}

{{{id=13|
T3 = S.hecke_matrix(3)
///
}}}

{{{id=10|
eta3 = T3 - (1+db3*3)
///
}}}

{{{id=11|
eta3.det().factor()
///
2^30 * 3^4 * 7^2 * 43^2 * 17837^2
}}}

{{{id=12|
def eta(ell):
    T = S.hecke_matrix(ell)
    dbd = S.diamond_bracket_operator(ell).matrix()
    return T - (1 + dbd * ell)
///
}}}

{{{id=14|
eta(3).det().factor()
///
2^30 * 3^4 * 7^2 * 43^2 * 17837^2
}}}

{{{id=15|
eta(5).det().factor()
///
2^24 * 3^8 * 7^6 * 13^4 * 43^2 * 17837^2
}}}

{{{id=16|
eta(7).det().factor()
///
2^34 * 3^4 * 7^2 * 43^4 * 113^2 * 463^2 * 17837^2
}}}

{{{id=17|
eta(11).det().factor()
///
2^24 * 3^2 * 5^2 * 7^8 * 17^2 * 43^2 * 1933^2 * 17837^2 * 28547^2
}}}

{{{id=18|
eta(13).det().factor()
///
2^24 * 3^4 * 5^4 * 7^2 * 31^2 * 43^2 * 2521^2 * 17837^2 * 7334699^2
}}}

{{{id=19|
time phi = S.integral_period_mapping()
///
Time: CPU 0.00 s, Wall: 0.00 s
}}}

{{{id=20|
phi(M.0).denominator().factor()
///
2^2 * 3 * 7^2 * 43 * 17837
}}}

{{{id=21|
e3 = eta(3).change_ring(ZZ); e3
///
44 x 44 dense matrix over Integer Ring (type 'print e3.str()' to see all of the entries)
}}}

{{{id=22|
s = eta(3)
///
}}}

{{{id=23|
E = End(ZZ^44)
///
}}}

{{{id=28|
psi = E(eta(3))
///
}}}

{{{id=29|
Q0 = psi.codomain() / psi.image()
///
}}}

{{{id=30|
Q0.cardinality().factor()
///
2^30 * 3^4 * 7^2 * 43^2 * 17837^2
}}}

{{{id=32|
Q0
///
Finitely generated module V/W over Integer Ring with invariants (4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 386563464, 386563464)
}}}

{{{id=33|
E0 = End(Q0); E0
///
Set of Morphisms from Finitely generated module V/W over Integer Ring with invariants (4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 386563464, 386563464) to Finitely generated module V/W over Integer Ring with invariants (4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 386563464, 386563464) in Category of modules over Integer Ring
}}}

{{{id=37|
psi = E(eta(5))
///
}}}

{{{id=38|
E0.hom(
///
}}}

{{{id=39|
im_gens = [Q0(psi(x.lift())) for x in Q0.gens()]; im_gens
///
[(0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 193281732), (0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 193281732, 193281732), (0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 193281732, 0), (0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 193281732, 0), (0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 193281732, 0), (0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 193281732, 0), (0, 0, 0, 0, 2, 0, 4, 2, 0, 0, 193281732, 0), (0, 0, 0, 0, 0, 2, 6, 4, 0, 0, 289922598, 0), (2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 289922598, 193281732), (0, 0, 0, 0, 2, 2, 2, 4, 4, 2, 96640866, 96640866), (0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 96640866, 0), (2, 0, 2, 2, 0, 2, 2, 4, 6, 0, 193281732, 0)]
}}}

{{{id=36|
psi5 = Q0.hom(im_gens)
///
}}}

{{{id=35|
E5 = psi5.kernel(); E5
///
Finitely generated module V/W over Integer Ring with invariants (2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 193281732, 193281732)
}}}

{{{id=41|
psi = E(eta(7))
im_gens = [Q0(psi(x.lift())) for x in Q0.gens()]
psi_mod = E5.hom(im_gens)
E7 = psi_mod.kernel()
///
}}}

{{{id=42|
E7
///
Finitely generated module V/W over Integer Ring with invariants (2, 2, 2, 2, 32213622, 32213622)
}}}

{{{id=43|
E7.cardinality().factor()
///
2^6 * 3^2 * 7^2 * 43^2 * 17837^2
}}}

{{{id=44|
%time
psi = E(eta(11))
im_gens = [Q0(psi(x.lift())) for x in E7.gens()]
psi_mod = E7.hom(im_gens)
E11 = psi_mod.kernel()
///
CPU time: 1.06 s,  Wall time: 1.06 s
}}}

{{{id=45|
E11.cardinality().factor()
///
2^6 * 3^2 * 7^2 * 43^2 * 17837^2
}}}

{{{id=46|
eta(11).det().factor()
///
2^24 * 3^2 * 5^2 * 7^8 * 17^2 * 43^2 * 1933^2 * 17837^2 * 28547^2
}}}

{{{id=51|
dimension_cusp_forms(Gamma1(29))
///
22
}}}

{{{id=50|

///
}}}

{{{id=49|

///
}}}

{{{id=48|

///
}}}

{{{id=47|

///
}}}