[N,k,chi] = [1110,4,Mod(1,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, 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("1110.1");
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
\(2\)
\(1\)
\(3\)
\(-1\)
\(5\)
\(-1\)
\(37\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{7}^{3} + 12T_{7}^{2} - 75T_{7} - 150 \)
T7^3 + 12*T7^2 - 75*T7 - 150
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1110))\).
$p$
$F_p(T)$
$2$
\( (T + 2)^{3} \)
(T + 2)^3
$3$
\( (T - 3)^{3} \)
(T - 3)^3
$5$
\( (T - 5)^{3} \)
(T - 5)^3
$7$
\( T^{3} + 12 T^{2} - 75 T - 150 \)
T^3 + 12*T^2 - 75*T - 150
$11$
\( T^{3} - 9 T^{2} - 1473 T + 10348 \)
T^3 - 9*T^2 - 1473*T + 10348
$13$
\( T^{3} + 33 T^{2} + 315 T + 683 \)
T^3 + 33*T^2 + 315*T + 683
$17$
\( T^{3} + 105 T^{2} + 1755 T - 16714 \)
T^3 + 105*T^2 + 1755*T - 16714
$19$
\( T^{3} + 81 T^{2} - 6663 T + 45506 \)
T^3 + 81*T^2 - 6663*T + 45506
$23$
\( T^{3} + 60 T^{2} - 26235 T + 971914 \)
T^3 + 60*T^2 - 26235*T + 971914
$29$
\( T^{3} + 108 T^{2} - 25512 T - 2931869 \)
T^3 + 108*T^2 - 25512*T - 2931869
$31$
\( T^{3} + 342 T^{2} + 23403 T + 451090 \)
T^3 + 342*T^2 + 23403*T + 451090
$37$
\( (T - 37)^{3} \)
(T - 37)^3
$41$
\( T^{3} + 600 T^{2} + \cdots - 19235660 \)
T^3 + 600*T^2 + 26343*T - 19235660
$43$
\( T^{3} - 90 T^{2} - 56496 T + 6229221 \)
T^3 - 90*T^2 - 56496*T + 6229221
$47$
\( T^{3} + 237 T^{2} + \cdots - 34912209 \)
T^3 + 237*T^2 - 151509*T - 34912209
$53$
\( T^{3} - 63 T^{2} - 175284 T - 22299408 \)
T^3 - 63*T^2 - 175284*T - 22299408
$59$
\( T^{3} + 264 T^{2} + \cdots - 34412507 \)
T^3 + 264*T^2 - 372264*T - 34412507
$61$
\( T^{3} + 732 T^{2} + \cdots + 10980910 \)
T^3 + 732*T^2 + 164853*T + 10980910
$67$
\( T^{3} + 867 T^{2} + \cdots + 13712260 \)
T^3 + 867*T^2 + 214983*T + 13712260
$71$
\( T^{3} + 1233 T^{2} + \cdots - 331049044 \)
T^3 + 1233*T^2 - 91437*T - 331049044
$73$
\( T^{3} + 837 T^{2} + \cdots - 789421254 \)
T^3 + 837*T^2 - 952347*T - 789421254
$79$
\( T^{3} + 1053 T^{2} + \cdots - 164141764 \)
T^3 + 1053*T^2 - 214683*T - 164141764
$83$
\( T^{3} - 312 T^{2} + \cdots + 137107175 \)
T^3 - 312*T^2 - 445440*T + 137107175
$89$
\( T^{3} - 495 T^{2} + \cdots - 193482029 \)
T^3 - 495*T^2 - 881085*T - 193482029
$97$
\( T^{3} + 1092 T^{2} + \cdots - 312757294 \)
T^3 + 1092*T^2 - 553707*T - 312757294
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