[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
\( T_{5}^{3} - 249T_{5} - 392 \)
T5^3 - 249*T5 - 392
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
$5$
\( T^{3} - 249T - 392 \)
T^3 - 249*T - 392
$7$
\( (T + 7)^{3} \)
(T + 7)^3
$11$
\( T^{3} - 11 T^{2} - 4040 T + 90276 \)
T^3 - 11*T^2 - 4040*T + 90276
$13$
\( (T + 13)^{3} \)
(T + 13)^3
$17$
\( T^{3} + 23 T^{2} - 10014 T - 401136 \)
T^3 + 23*T^2 - 10014*T - 401136
$19$
\( T^{3} + 38 T^{2} - 2187 T - 54960 \)
T^3 + 38*T^2 - 2187*T - 54960
$23$
\( T^{3} + 44 T^{2} - 16613 T - 693984 \)
T^3 + 44*T^2 - 16613*T - 693984
$29$
\( T^{3} + 328 T^{2} - 18091 T - 9415330 \)
T^3 + 328*T^2 - 18091*T - 9415330
$31$
\( T^{3} - 159 T^{2} - 22908 T + 3244544 \)
T^3 - 159*T^2 - 22908*T + 3244544
$37$
\( T^{3} + 227 T^{2} + \cdots - 10740408 \)
T^3 + 227*T^2 - 47682*T - 10740408
$41$
\( T^{3} + 10 T^{2} - 9768 T - 380352 \)
T^3 + 10*T^2 - 9768*T - 380352
$43$
\( T^{3} - 10 T^{2} - 111571 T - 7537124 \)
T^3 - 10*T^2 - 111571*T - 7537124
$47$
\( T^{3} + 309 T^{2} + \cdots - 12122992 \)
T^3 + 309*T^2 - 111594*T - 12122992
$53$
\( T^{3} + 849 T^{2} + \cdots + 12064716 \)
T^3 + 849*T^2 + 208932*T + 12064716
$59$
\( T^{3} - 34 T^{2} + \cdots - 136093440 \)
T^3 - 34*T^2 - 549848*T - 136093440
$61$
\( T^{3} - 201 T^{2} + \cdots - 33416452 \)
T^3 - 201*T^2 - 458736*T - 33416452
$67$
\( T^{3} + 308 T^{2} - 100420 T + 5195248 \)
T^3 + 308*T^2 - 100420*T + 5195248
$71$
\( T^{3} + 66 T^{2} + \cdots - 213395392 \)
T^3 + 66*T^2 - 777000*T - 213395392
$73$
\( T^{3} - 1270 T^{2} + \cdots - 47910282 \)
T^3 - 1270*T^2 + 449215*T - 47910282
$79$
\( T^{3} - 2947 T^{2} + \cdots - 887673120 \)
T^3 - 2947*T^2 + 2828578*T - 887673120
$83$
\( T^{3} - 1505 T^{2} + \cdots + 663722676 \)
T^3 - 1505*T^2 - 183036*T + 663722676
$89$
\( T^{3} - 2153 T^{2} + \cdots + 2003051400 \)
T^3 - 2153*T^2 - 385854*T + 2003051400
$97$
\( T^{3} + 1393 T^{2} + \cdots - 4407218284 \)
T^3 + 1393*T^2 - 3230392*T - 4407218284
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