[N,k,chi] = [671,2,Mod(1,671)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(671, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("671.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Newform invariants
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
Refresh table
\( p \)
Sign
\(11\)
\(1\)
\(61\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{6} - 7T_{2}^{4} + 2T_{2}^{3} + 12T_{2}^{2} - 5T_{2} - 2 \)
T2^6 - 7*T2^4 + 2*T2^3 + 12*T2^2 - 5*T2 - 2
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(671))\).
$p$
$F_p(T)$
$2$
\( T^{6} - 7 T^{4} + 2 T^{3} + 12 T^{2} + \cdots - 2 \)
T^6 - 7*T^4 + 2*T^3 + 12*T^2 - 5*T - 2
$3$
\( T^{6} + T^{5} - 6 T^{4} - 3 T^{3} + 9 T^{2} + \cdots - 1 \)
T^6 + T^5 - 6*T^4 - 3*T^3 + 9*T^2 + T - 1
$5$
\( T^{6} + T^{5} - 9 T^{4} - 3 T^{3} + 6 T^{2} + \cdots - 1 \)
T^6 + T^5 - 9*T^4 - 3*T^3 + 6*T^2 + T - 1
$7$
\( T^{6} + 5 T^{5} + 4 T^{4} - 11 T^{3} + \cdots + 4 \)
T^6 + 5*T^5 + 4*T^4 - 11*T^3 - 13*T^2 + 3*T + 4
$11$
\( (T + 1)^{6} \)
(T + 1)^6
$13$
\( T^{6} + 4 T^{5} - 12 T^{4} - 63 T^{3} + \cdots + 2 \)
T^6 + 4*T^5 - 12*T^4 - 63*T^3 - 36*T^2 + 55*T + 2
$17$
\( T^{6} + 5 T^{5} - 39 T^{4} - 143 T^{3} + \cdots - 926 \)
T^6 + 5*T^5 - 39*T^4 - 143*T^3 + 328*T^2 + 563*T - 926
$19$
\( T^{6} + 3 T^{5} - 9 T^{4} - 40 T^{3} + \cdots - 2 \)
T^6 + 3*T^5 - 9*T^4 - 40*T^3 - 43*T^2 - 17*T - 2
$23$
\( T^{6} + 3 T^{5} - 43 T^{4} - 74 T^{3} + \cdots + 131 \)
T^6 + 3*T^5 - 43*T^4 - 74*T^3 + 136*T^2 + 298*T + 131
$29$
\( T^{6} + T^{5} - 9 T^{4} - 12 T^{3} + \cdots - 2 \)
T^6 + T^5 - 9*T^4 - 12*T^3 + 7*T^2 + 7*T - 2
$31$
\( T^{6} + 10 T^{5} + 25 T^{4} - 21 T^{3} + \cdots + 7 \)
T^6 + 10*T^5 + 25*T^4 - 21*T^3 - 142*T^2 - 124*T + 7
$37$
\( T^{6} + 19 T^{5} + 32 T^{4} + \cdots - 2993 \)
T^6 + 19*T^5 + 32*T^4 - 1233*T^3 - 8111*T^2 - 15211*T - 2993
$41$
\( T^{6} + 7 T^{5} - 89 T^{4} - 204 T^{3} + \cdots + 724 \)
T^6 + 7*T^5 - 89*T^4 - 204*T^3 + 497*T^2 + 1331*T + 724
$43$
\( T^{6} + 2 T^{5} - 74 T^{4} + 155 T^{3} + \cdots - 2 \)
T^6 + 2*T^5 - 74*T^4 + 155*T^3 + 108*T^2 - 299*T - 2
$47$
\( T^{6} - 5 T^{5} - 110 T^{4} + \cdots - 26800 \)
T^6 - 5*T^5 - 110*T^4 + 469*T^3 + 2959*T^2 - 7745*T - 26800
$53$
\( T^{6} + 9 T^{5} - 82 T^{4} + \cdots - 1714 \)
T^6 + 9*T^5 - 82*T^4 - 579*T^3 + 2143*T^2 + 6301*T - 1714
$59$
\( T^{6} + 5 T^{5} - 59 T^{4} + \cdots - 4793 \)
T^6 + 5*T^5 - 59*T^4 - 174*T^3 + 1176*T^2 + 782*T - 4793
$61$
\( (T + 1)^{6} \)
(T + 1)^6
$67$
\( T^{6} + 14 T^{5} - 57 T^{4} + \cdots - 27503 \)
T^6 + 14*T^5 - 57*T^4 - 1956*T^3 - 12473*T^2 - 31690*T - 27503
$71$
\( T^{6} + 14 T^{5} - 56 T^{4} + \cdots - 10877 \)
T^6 + 14*T^5 - 56*T^4 - 726*T^3 + 911*T^2 + 6679*T - 10877
$73$
\( T^{6} + 14 T^{5} - 200 T^{4} + \cdots + 467006 \)
T^6 + 14*T^5 - 200*T^4 - 3277*T^3 + 5248*T^2 + 186509*T + 467006
$79$
\( T^{6} - 5 T^{5} - 163 T^{4} + \cdots - 80764 \)
T^6 - 5*T^5 - 163*T^4 + 726*T^3 + 7457*T^2 - 24793*T - 80764
$83$
\( T^{6} - 17 T^{5} - 171 T^{4} + \cdots - 59872 \)
T^6 - 17*T^5 - 171*T^4 + 2774*T^3 + 8471*T^2 - 71253*T - 59872
$89$
\( T^{6} + 25 T^{5} + 115 T^{4} + \cdots - 547 \)
T^6 + 25*T^5 + 115*T^4 - 144*T^3 - 740*T^2 + 1298*T - 547
$97$
\( T^{6} + 24 T^{5} + 96 T^{4} + \cdots + 24269 \)
T^6 + 24*T^5 + 96*T^4 - 1267*T^3 - 7791*T^2 + 7232*T + 24269
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