[N,k,chi] = [462,8,Mod(1,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("462.1");
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
\(2\)
\(1\)
\(3\)
\(1\)
\(7\)
\(1\)
\(11\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{4} - 238T_{5}^{3} - 75595T_{5}^{2} + 5065900T_{5} - 77962500 \)
T5^4 - 238*T5^3 - 75595*T5^2 + 5065900*T5 - 77962500
acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(462))\).
$p$
$F_p(T)$
$2$
\( (T + 8)^{4} \)
(T + 8)^4
$3$
\( (T + 27)^{4} \)
(T + 27)^4
$5$
\( T^{4} - 238 T^{3} + \cdots - 77962500 \)
T^4 - 238*T^3 - 75595*T^2 + 5065900*T - 77962500
$7$
\( (T + 343)^{4} \)
(T + 343)^4
$11$
\( (T + 1331)^{4} \)
(T + 1331)^4
$13$
\( T^{4} + \cdots + 995662722767604 \)
T^4 - 8498*T^3 - 106025095*T^2 + 358032991508*T + 995662722767604
$17$
\( T^{4} - 27566 T^{3} + \cdots + 17\!\cdots\!80 \)
T^4 - 27566*T^3 - 676457352*T^2 + 12046125771992*T + 175475829035464880
$19$
\( T^{4} + 21084 T^{3} + \cdots - 25\!\cdots\!76 \)
T^4 + 21084*T^3 - 393164073*T^2 + 1805772539448*T - 2542485844197576
$23$
\( T^{4} + 95782 T^{3} + \cdots - 33\!\cdots\!20 \)
T^4 + 95782*T^3 - 478407412*T^2 - 165426946916608*T - 330306008108925120
$29$
\( T^{4} - 45710 T^{3} + \cdots + 58\!\cdots\!72 \)
T^4 - 45710*T^3 - 52312509643*T^2 - 130259448717580*T + 58527616034973179172
$31$
\( T^{4} - 72718 T^{3} + \cdots - 67\!\cdots\!00 \)
T^4 - 72718*T^3 - 19087743396*T^2 + 2330888553063536*T - 67944376758500895200
$37$
\( T^{4} - 23374 T^{3} + \cdots + 16\!\cdots\!52 \)
T^4 - 23374*T^3 - 259902840675*T^2 + 2988234416090732*T + 16641836594284394120452
$41$
\( T^{4} - 373072 T^{3} + \cdots + 49\!\cdots\!00 \)
T^4 - 373072*T^3 - 558747296580*T^2 + 171710088385193200*T + 49368651666771395960000
$43$
\( T^{4} - 446426 T^{3} + \cdots - 30\!\cdots\!96 \)
T^4 - 446426*T^3 - 555376613988*T^2 + 288386894235670208*T - 30649943728640782669696
$47$
\( T^{4} - 941208 T^{3} + \cdots - 63\!\cdots\!68 \)
T^4 - 941208*T^3 - 291485184861*T^2 + 329714885076865184*T - 6383446613216185210968
$53$
\( T^{4} - 1656110 T^{3} + \cdots - 26\!\cdots\!12 \)
T^4 - 1656110*T^3 - 2595753970616*T^2 + 6023415605863048680*T - 2651254403473258384272912
$59$
\( T^{4} + 1211724 T^{3} + \cdots + 15\!\cdots\!80 \)
T^4 + 1211724*T^3 - 8647117920801*T^2 - 6840572327924495832*T + 15456574744791072595048080
$61$
\( T^{4} - 865552 T^{3} + \cdots + 48\!\cdots\!40 \)
T^4 - 865552*T^3 - 8864622108408*T^2 + 5622014249629621376*T + 4867854870053795494972240
$67$
\( T^{4} + 2542132 T^{3} + \cdots - 54\!\cdots\!52 \)
T^4 + 2542132*T^3 - 5328632136153*T^2 - 12490526499801566904*T - 5429037662605425538711152
$71$
\( T^{4} + 3417148 T^{3} + \cdots + 72\!\cdots\!40 \)
T^4 + 3417148*T^3 - 30173090103552*T^2 - 95992811696859579968*T + 72020957853682099423939840
$73$
\( T^{4} + 3507490 T^{3} + \cdots - 30\!\cdots\!52 \)
T^4 + 3507490*T^3 - 5176864097231*T^2 - 21164887939405447860*T - 3024970198400188023989652
$79$
\( T^{4} + 12775068 T^{3} + \cdots + 87\!\cdots\!00 \)
T^4 + 12775068*T^3 + 59336902721072*T^2 + 119285081131755025536*T + 87786460694535012738316800
$83$
\( T^{4} + 5186874 T^{3} + \cdots - 17\!\cdots\!44 \)
T^4 + 5186874*T^3 - 6266416980988*T^2 - 15936041350441107216*T - 1778075809782835608565344
$89$
\( T^{4} + 7441292 T^{3} + \cdots - 22\!\cdots\!28 \)
T^4 + 7441292*T^3 - 133169310303120*T^2 - 1170732230955399406320*T - 2238513940795714926433090128
$97$
\( T^{4} - 355374 T^{3} + \cdots - 68\!\cdots\!24 \)
T^4 - 355374*T^3 - 115292338553232*T^2 - 567365308944945956536*T - 680602520438220040792810224
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