[N,k,chi] = [126,16,Mod(1,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.1");
S:= CuspForms(chi, 16);
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
\(2\)
\(1\)
\(3\)
\(1\)
\(7\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{4} + 291312T_{5}^{3} - 37767651840T_{5}^{2} - 9508350109406400T_{5} + 127810130166316422000 \)
T5^4 + 291312*T5^3 - 37767651840*T5^2 - 9508350109406400*T5 + 127810130166316422000
acting on \(S_{16}^{\mathrm{new}}(\Gamma_0(126))\).
$p$
$F_p(T)$
$2$
\( (T + 128)^{4} \)
(T + 128)^4
$3$
\( T^{4} \)
T^4
$5$
\( T^{4} + 291312 T^{3} + \cdots + 12\!\cdots\!00 \)
T^4 + 291312*T^3 - 37767651840*T^2 - 9508350109406400*T + 127810130166316422000
$7$
\( (T - 823543)^{4} \)
(T - 823543)^4
$11$
\( T^{4} + 121144752 T^{3} + \cdots + 27\!\cdots\!00 \)
T^4 + 121144752*T^3 - 9478777058508384*T^2 - 920489047162536010484160*T + 27609685777642412216072445116400
$13$
\( T^{4} - 170165240 T^{3} + \cdots + 16\!\cdots\!12 \)
T^4 - 170165240*T^3 - 92767919190612744*T^2 + 11369884252285006315512736*T + 1616204088795405696273728214074512
$17$
\( T^{4} + 345685200 T^{3} + \cdots - 11\!\cdots\!48 \)
T^4 + 345685200*T^3 - 6582068697746635776*T^2 + 5905214183873332421331392448*T - 1180276839098043826292898234951055248
$19$
\( T^{4} - 4738793696 T^{3} + \cdots + 11\!\cdots\!56 \)
T^4 - 4738793696*T^3 - 4954085492089713312*T^2 + 1038144106594179719832925696*T + 1120570268318063758395954078918297856
$23$
\( T^{4} + 17023827024 T^{3} + \cdots + 86\!\cdots\!00 \)
T^4 + 17023827024*T^3 - 441477548761914097920*T^2 + 772948746937326426869733469632*T + 8619545918600585841421078805390603698800
$29$
\( T^{4} + 96242392128 T^{3} + \cdots + 14\!\cdots\!72 \)
T^4 + 96242392128*T^3 - 28476418234416074194752*T^2 - 1494250247378200415035869122383872*T + 147965243258867365367625709114083653700943872
$31$
\( T^{4} - 65665329632 T^{3} + \cdots + 80\!\cdots\!48 \)
T^4 - 65665329632*T^3 - 26018906244988802111904*T^2 + 638497607650713890054481363031552*T + 80061247230750472868327330621408850287573248
$37$
\( T^{4} - 279650496248 T^{3} + \cdots + 24\!\cdots\!20 \)
T^4 - 279650496248*T^3 - 492030874927082690235912*T^2 + 137033732428711961162796821734312864*T + 24314362665122810421207173530529117634967115920
$41$
\( T^{4} + 274507805040 T^{3} + \cdots - 33\!\cdots\!60 \)
T^4 + 274507805040*T^3 - 1266787014015745260545472*T^2 + 503585871074979004804910200067605824*T - 33089241545416739986611703387503885471786690960
$43$
\( T^{4} - 1551932654480 T^{3} + \cdots + 51\!\cdots\!96 \)
T^4 - 1551932654480*T^3 - 3019786256629762187194272*T^2 + 3403439993109964681289357264320833280*T + 513963665078277370397950413539262643141302436096
$47$
\( T^{4} + 686050223712 T^{3} + \cdots - 52\!\cdots\!20 \)
T^4 + 686050223712*T^3 - 31490593241474484255214080*T^2 - 84437934069415161410080877528643534336*T - 52823215449856663764448317959535886255751456037120
$53$
\( T^{4} + 4929897017760 T^{3} + \cdots + 47\!\cdots\!96 \)
T^4 + 4929897017760*T^3 - 47200108040407369883680128*T^2 - 137392022850016745044284765631422128640*T + 471747677623437137122824737417432534378404770045696
$59$
\( T^{4} + 15661604798112 T^{3} + \cdots + 82\!\cdots\!04 \)
T^4 + 15661604798112*T^3 - 15852219090300881303914368*T^2 - 497068504653323823127239849564769473024*T + 823589827463570433559876513531365521743821998939904
$61$
\( T^{4} - 7270740102248 T^{3} + \cdots + 61\!\cdots\!36 \)
T^4 - 7270740102248*T^3 - 758840830961982698764160328*T^2 - 1856746856001685590418815978791241332768*T + 617874712130261916163427431175463152740881405813136
$67$
\( T^{4} - 2642113680560 T^{3} + \cdots + 17\!\cdots\!20 \)
T^4 - 2642113680560*T^3 - 255520158493981389771947808*T^2 - 447345829588002830138299149956296746752*T + 1762177733962989599511228744689478138421986196568320
$71$
\( T^{4} + 62559334721520 T^{3} + \cdots + 11\!\cdots\!00 \)
T^4 + 62559334721520*T^3 - 16171164815478593661553123584*T^2 - 687067912208597469021342702626147754528960*T + 11059752438274439079911961695674216651985438775907244400
$73$
\( T^{4} + 53486860270312 T^{3} + \cdots + 84\!\cdots\!20 \)
T^4 + 53486860270312*T^3 - 27458315104201484994527984040*T^2 - 1450896345454047537918242378128952160938336*T + 84307634396481808422021170201638784368690377939303131920
$79$
\( T^{4} - 77560377412544 T^{3} + \cdots - 35\!\cdots\!44 \)
T^4 - 77560377412544*T^3 - 53320826942686901944877515392*T^2 - 282548540190461322025406763396813668274176*T - 357090531097153963518124372036215403179028390220754944
$83$
\( T^{4} - 58088393760768 T^{3} + \cdots - 14\!\cdots\!00 \)
T^4 - 58088393760768*T^3 - 63470047487125010460616986624*T^2 - 5938839059582010955054043745080830517575680*T - 143290733096567110195109369546571064327124494416504422400
$89$
\( T^{4} - 296914762526928 T^{3} + \cdots - 76\!\cdots\!32 \)
T^4 - 296914762526928*T^3 + 22758929881029669602425104576*T^2 + 449114653570725670429115802541923125663808*T - 76000402820785307150249453533674422403359208204929791632
$97$
\( T^{4} + \cdots - 66\!\cdots\!76 \)
T^4 - 1391306483388248*T^3 - 641576592688491400587334127400*T^2 + 587778732284000384148008165751743448134892448*T - 66493305593830870723095792945696536556877502723085694977776
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