[N,k,chi] = [546,4,Mod(1,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.1");
S:= CuspForms(chi, 4);
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
\(2\)
\(1\)
\(3\)
\(-1\)
\(7\)
\(-1\)
\(13\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{3} - 13T_{5}^{2} - 146T_{5} - 288 \)
T5^3 - 13*T5^2 - 146*T5 - 288
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(546))\).
$p$
$F_p(T)$
$2$
\( (T + 2)^{3} \)
(T + 2)^3
$3$
\( (T - 3)^{3} \)
(T - 3)^3
$5$
\( T^{3} - 13 T^{2} - 146 T - 288 \)
T^3 - 13*T^2 - 146*T - 288
$7$
\( (T - 7)^{3} \)
(T - 7)^3
$11$
\( T^{3} - 17 T^{2} - 2310 T - 10536 \)
T^3 - 17*T^2 - 2310*T - 10536
$13$
\( (T + 13)^{3} \)
(T + 13)^3
$17$
\( T^{3} - 89 T^{2} - 3436 T + 16628 \)
T^3 - 89*T^2 - 3436*T + 16628
$19$
\( T^{3} - 89 T^{2} - 9756 T + 718176 \)
T^3 - 89*T^2 - 9756*T + 718176
$23$
\( T^{3} - 289 T^{2} + 12948 T + 563424 \)
T^3 - 289*T^2 + 12948*T + 563424
$29$
\( T^{3} - 125 T^{2} - 29736 T + 2752572 \)
T^3 - 125*T^2 - 29736*T + 2752572
$31$
\( T^{3} + 208 T^{2} + 7760 T - 239488 \)
T^3 + 208*T^2 + 7760*T - 239488
$37$
\( T^{3} - 213 T^{2} - 54852 T + 5144564 \)
T^3 - 213*T^2 - 54852*T + 5144564
$41$
\( T^{3} - 530 T^{2} + \cdots + 18905088 \)
T^3 - 530*T^2 - 6176*T + 18905088
$43$
\( T^{3} + 75 T^{2} - 198672 T + 1482192 \)
T^3 + 75*T^2 - 198672*T + 1482192
$47$
\( T^{3} - 298 T^{2} + \cdots + 62195328 \)
T^3 - 298*T^2 - 206040*T + 62195328
$53$
\( T^{3} - 710 T^{2} + 108476 T - 1248616 \)
T^3 - 710*T^2 + 108476*T - 1248616
$59$
\( T^{3} + 250 T^{2} + \cdots - 14803488 \)
T^3 + 250*T^2 - 63152*T - 14803488
$61$
\( T^{3} + 511 T^{2} + \cdots - 63342772 \)
T^3 + 511*T^2 - 131368*T - 63342772
$67$
\( T^{3} + 522 T^{2} - 115704 T - 7056512 \)
T^3 + 522*T^2 - 115704*T - 7056512
$71$
\( T^{3} - 282 T^{2} + \cdots - 150609024 \)
T^3 - 282*T^2 - 906696*T - 150609024
$73$
\( T^{3} + 701 T^{2} + \cdots - 298076364 \)
T^3 + 701*T^2 - 490416*T - 298076364
$79$
\( T^{3} - 1262 T^{2} + \cdots + 144063488 \)
T^3 - 1262*T^2 + 123872*T + 144063488
$83$
\( T^{3} - 1700 T^{2} + \cdots - 161161584 \)
T^3 - 1700*T^2 + 923292*T - 161161584
$89$
\( T^{3} - 1628 T^{2} + \cdots - 32164336 \)
T^3 - 1628*T^2 + 645164*T - 32164336
$97$
\( T^{3} - 1526 T^{2} + \cdots + 199579224 \)
T^3 - 1526*T^2 - 225732*T + 199579224
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