[N,k,chi] = [14,14,Mod(1,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14.1");
S:= CuspForms(chi, 14);
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
sage: f.q_expansion() # note that sage often uses an isomorphic number field
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{78985}\).
We also show the integral \(q\)-expansion of the trace form .
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
\(2\)
\(-1\)
\(7\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} - 1106T_{3} - 1668816 \)
T3^2 - 1106*T3 - 1668816
acting on \(S_{14}^{\mathrm{new}}(\Gamma_0(14))\).
$p$
$F_p(T)$
$2$
\( (T - 64)^{2} \)
(T - 64)^2
$3$
\( T^{2} - 1106 T - 1668816 \)
T^2 - 1106*T - 1668816
$5$
\( T^{2} - 75530 T + 1306059040 \)
T^2 - 75530*T + 1306059040
$7$
\( (T + 117649)^{2} \)
(T + 117649)^2
$11$
\( T^{2} - 3335860 T - 92049177677600 \)
T^2 - 3335860*T - 92049177677600
$13$
\( T^{2} + \cdots - 292295968590024 \)
T^2 - 7998102*T - 292295968590024
$17$
\( T^{2} - 39024832 T - 97\!\cdots\!44 \)
T^2 - 39024832*T - 9758706249881444
$19$
\( T^{2} - 124092934 T - 19\!\cdots\!36 \)
T^2 - 124092934*T - 19512281879877536
$23$
\( T^{2} - 1900816000 T + 88\!\cdots\!00 \)
T^2 - 1900816000*T + 887383104740704000
$29$
\( T^{2} + 245135152 T - 89\!\cdots\!24 \)
T^2 + 245135152*T - 8995562472011542724
$31$
\( T^{2} + 11010560148 T + 23\!\cdots\!76 \)
T^2 + 11010560148*T + 23518457897478458976
$37$
\( T^{2} + 39630491216 T + 28\!\cdots\!64 \)
T^2 + 39630491216*T + 287583855592486811164
$41$
\( T^{2} + 2431027368 T - 46\!\cdots\!44 \)
T^2 + 2431027368*T - 4678961326726666644
$43$
\( T^{2} - 17823138316 T - 24\!\cdots\!36 \)
T^2 - 17823138316*T - 2410629842009246817536
$47$
\( T^{2} - 64488311076 T - 86\!\cdots\!56 \)
T^2 - 64488311076*T - 8625785893407834577056
$53$
\( T^{2} + 126504176628 T - 39\!\cdots\!04 \)
T^2 + 126504176628*T - 3981666841616964061404
$59$
\( T^{2} - 341259961238 T - 34\!\cdots\!64 \)
T^2 - 341259961238*T - 34319603409494825688464
$61$
\( T^{2} - 447240700746 T + 20\!\cdots\!04 \)
T^2 - 447240700746*T + 20017224782231037579504
$67$
\( T^{2} + 2071322290888 T + 10\!\cdots\!36 \)
T^2 + 2071322290888*T + 1015957028588554010853136
$71$
\( T^{2} - 650434465720 T - 84\!\cdots\!00 \)
T^2 - 650434465720*T - 84525284974530429286400
$73$
\( T^{2} + 1449809330116 T - 11\!\cdots\!36 \)
T^2 + 1449809330116*T - 116212848736305069242636
$79$
\( T^{2} - 1525152397656 T - 15\!\cdots\!16 \)
T^2 - 1525152397656*T - 1515909112419346824940416
$83$
\( T^{2} - 4257517639438 T - 38\!\cdots\!64 \)
T^2 - 4257517639438*T - 3825316175555834366917664
$89$
\( T^{2} - 12593651222628 T + 39\!\cdots\!96 \)
T^2 - 12593651222628*T + 39328208522091210467230596
$97$
\( T^{2} + 16541570007760 T + 28\!\cdots\!00 \)
T^2 + 16541570007760*T + 28182735553043619519115900
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