[N,k,chi] = [414,8,Mod(1,414)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(414, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("414.1");
S:= CuspForms(chi, 8);
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
\(2\)
\(1\)
\(3\)
\(-1\)
\(23\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{3} + 92T_{5}^{2} - 27896T_{5} - 1245480 \)
T5^3 + 92*T5^2 - 27896*T5 - 1245480
acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(414))\).
$p$
$F_p(T)$
$2$
\( (T + 8)^{3} \)
(T + 8)^3
$3$
\( T^{3} \)
T^3
$5$
\( T^{3} + 92 T^{2} - 27896 T - 1245480 \)
T^3 + 92*T^2 - 27896*T - 1245480
$7$
\( (T + 286)^{3} \)
(T + 286)^3
$11$
\( T^{3} - 1820 T^{2} + \cdots - 39808807752 \)
T^3 - 1820*T^2 - 27151880*T - 39808807752
$13$
\( T^{3} + 3698 T^{2} + \cdots - 31329885032 \)
T^3 + 3698*T^2 - 193598740*T - 31329885032
$17$
\( T^{3} + 3164 T^{2} + \cdots + 8811060158208 \)
T^3 + 3164*T^2 - 885465776*T + 8811060158208
$19$
\( T^{3} + 14234 T^{2} + \cdots - 27667220902592 \)
T^3 + 14234*T^2 - 1522071172*T - 27667220902592
$23$
\( (T - 12167)^{3} \)
(T - 12167)^3
$29$
\( T^{3} - 171914 T^{2} + \cdots + 62745468718728 \)
T^3 - 171914*T^2 + 965763532*T + 62745468718728
$31$
\( T^{3} + 124972 T^{2} + \cdots + 9840206494080 \)
T^3 + 124972*T^2 + 3227888208*T + 9840206494080
$37$
\( T^{3} + 679074 T^{2} + \cdots + 82\!\cdots\!28 \)
T^3 + 679074*T^2 + 137535024852*T + 8218633585606528
$41$
\( T^{3} - 331362 T^{2} + \cdots + 19\!\cdots\!64 \)
T^3 - 331362*T^2 - 138741876324*T + 19026129252033864
$43$
\( T^{3} + 145922 T^{2} + \cdots - 31\!\cdots\!92 \)
T^3 + 145922*T^2 - 805548853972*T - 318089312970964592
$47$
\( T^{3} - 1824192 T^{2} + \cdots + 86\!\cdots\!88 \)
T^3 - 1824192*T^2 + 30807861840*T + 860042320961666688
$53$
\( T^{3} - 3442448 T^{2} + \cdots + 55\!\cdots\!52 \)
T^3 - 3442448*T^2 + 2595290791576*T + 554036135891718552
$59$
\( T^{3} - 3147660 T^{2} + \cdots - 72\!\cdots\!28 \)
T^3 - 3147660*T^2 + 2792374232112*T - 728779539459774528
$61$
\( T^{3} + 3444530 T^{2} + \cdots - 29\!\cdots\!16 \)
T^3 + 3444530*T^2 + 161066020004*T - 2978436299977117616
$67$
\( T^{3} + 921870 T^{2} + \cdots - 21\!\cdots\!88 \)
T^3 + 921870*T^2 - 16596268766004*T - 21922248927159578288
$71$
\( T^{3} + 2594520 T^{2} + \cdots - 71\!\cdots\!68 \)
T^3 + 2594520*T^2 - 31981531975344*T - 71891896044666682368
$73$
\( T^{3} + 540826 T^{2} + \cdots - 39\!\cdots\!04 \)
T^3 + 540826*T^2 - 23336554754388*T - 39980794468341575304
$79$
\( T^{3} - 316994 T^{2} + \cdots + 11\!\cdots\!92 \)
T^3 - 316994*T^2 - 54946485342612*T + 110465781566770761192
$83$
\( T^{3} + 4119316 T^{2} + \cdots - 39\!\cdots\!52 \)
T^3 + 4119316*T^2 - 88578917675048*T - 390349097446304183352
$89$
\( T^{3} + 1417176 T^{2} + \cdots - 79\!\cdots\!12 \)
T^3 + 1417176*T^2 - 29947029212592*T - 79562620411640070912
$97$
\( T^{3} + 15089326 T^{2} + \cdots + 43\!\cdots\!24 \)
T^3 + 15089326*T^2 + 59585989673100*T + 43231364727590298024
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