[N,k,chi] = [251,2,Mod(1,251)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(251, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("251.1");
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
\(251\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{2} + T_{2} - 1 \)
T2^2 + T2 - 1
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(251))\).
$p$
$F_p(T)$
$2$
\( (T^{2} + T - 1)^{2} \)
(T^2 + T - 1)^2
$3$
\( T^{4} + 2 T^{3} - 2 T^{2} - 3 T + 1 \)
T^4 + 2*T^3 - 2*T^2 - 3*T + 1
$5$
\( T^{4} + 3 T^{3} - 2 T^{2} - 2 T + 1 \)
T^4 + 3*T^3 - 2*T^2 - 2*T + 1
$7$
\( T^{4} + 3 T^{3} - 5 T^{2} - 19 T - 11 \)
T^4 + 3*T^3 - 5*T^2 - 19*T - 11
$11$
\( T^{4} + 3 T^{3} - 4 T - 1 \)
T^4 + 3*T^3 - 4*T - 1
$13$
\( T^{4} + 12 T^{3} + 48 T^{2} + 77 T + 41 \)
T^4 + 12*T^3 + 48*T^2 + 77*T + 41
$17$
\( T^{4} - T^{3} - 24 T^{2} + 34 T + 31 \)
T^4 - T^3 - 24*T^2 + 34*T + 31
$19$
\( T^{4} + 9 T^{3} - 3 T^{2} - 89 T + 101 \)
T^4 + 9*T^3 - 3*T^2 - 89*T + 101
$23$
\( T^{4} - 4 T^{3} - 13 T^{2} + 34 T + 11 \)
T^4 - 4*T^3 - 13*T^2 + 34*T + 11
$29$
\( T^{4} + 12 T^{3} - T^{2} - 222 T + 311 \)
T^4 + 12*T^3 - T^2 - 222*T + 311
$31$
\( T^{4} + 2 T^{3} - 50 T^{2} - 51 T - 11 \)
T^4 + 2*T^3 - 50*T^2 - 51*T - 11
$37$
\( T^{4} + 13 T^{3} + 28 T^{2} + \cdots - 659 \)
T^4 + 13*T^3 + 28*T^2 - 192*T - 659
$41$
\( T^{4} - T^{3} - 35 T^{2} + 127 T - 121 \)
T^4 - T^3 - 35*T^2 + 127*T - 121
$43$
\( T^{4} + 5 T^{3} - 134 T^{2} + \cdots + 1439 \)
T^4 + 5*T^3 - 134*T^2 - 710*T + 1439
$47$
\( T^{4} - 12 T^{3} + 34 T^{2} - 13 T + 1 \)
T^4 - 12*T^3 + 34*T^2 - 13*T + 1
$53$
\( T^{4} - 5 T^{3} - 24 T^{2} + 80 T + 139 \)
T^4 - 5*T^3 - 24*T^2 + 80*T + 139
$59$
\( T^{4} - 6 T^{3} - 63 T^{2} + 116 T + 551 \)
T^4 - 6*T^3 - 63*T^2 + 116*T + 551
$61$
\( T^{4} + 21 T^{3} + 157 T^{2} + \cdots + 521 \)
T^4 + 21*T^3 + 157*T^2 + 489*T + 521
$67$
\( T^{4} - 17 T^{3} - 26 T^{2} + \cdots - 4159 \)
T^4 - 17*T^3 - 26*T^2 + 1382*T - 4159
$71$
\( T^{4} + 10 T^{3} - 74 T^{2} + \cdots + 2389 \)
T^4 + 10*T^3 - 74*T^2 - 495*T + 2389
$73$
\( T^{4} + 2 T^{3} - 130 T^{2} + \cdots + 539 \)
T^4 + 2*T^3 - 130*T^2 + 259*T + 539
$79$
\( T^{4} + 21 T^{3} - 20 T^{2} + \cdots - 13051 \)
T^4 + 21*T^3 - 20*T^2 - 2622*T - 13051
$83$
\( T^{4} + T^{3} - 210 T^{2} + 48 T + 6269 \)
T^4 + T^3 - 210*T^2 + 48*T + 6269
$89$
\( T^{4} - 5 T^{3} - 99 T^{2} + \cdots + 2489 \)
T^4 - 5*T^3 - 99*T^2 + 255*T + 2489
$97$
\( T^{4} - 6 T^{3} - 80 T^{2} - 58 T + 319 \)
T^4 - 6*T^3 - 80*T^2 - 58*T + 319
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