[N,k,chi] = [272,10,Mod(1,272)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(272, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("272.1");
S:= CuspForms(chi, 10);
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
\(2\)
\(-1\)
\(17\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{4} + 226T_{3}^{3} - 61062T_{3}^{2} - 14380776T_{3} - 384736824 \)
T3^4 + 226*T3^3 - 61062*T3^2 - 14380776*T3 - 384736824
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(272))\).
$p$
$F_p(T)$
$2$
\( T^{4} \)
T^4
$3$
\( T^{4} + 226 T^{3} + \cdots - 384736824 \)
T^4 + 226*T^3 - 61062*T^2 - 14380776*T - 384736824
$5$
\( T^{4} + 1656 T^{3} + \cdots + 2198652595200 \)
T^4 + 1656*T^3 - 5789580*T^2 - 8801246880*T + 2198652595200
$7$
\( T^{4} + 2654 T^{3} + \cdots - 39487188537440 \)
T^4 + 2654*T^3 - 28097010*T^2 - 69163409728*T - 39487188537440
$11$
\( T^{4} + 128106 T^{3} + \cdots - 84\!\cdots\!20 \)
T^4 + 128106*T^3 + 1709003874*T^2 - 279415051324776*T - 8431982321250069720
$13$
\( T^{4} + 16840 T^{3} + \cdots + 22\!\cdots\!92 \)
T^4 + 16840*T^3 - 14472407124*T^2 - 496616499359216*T + 2294755861786900192
$17$
\( (T + 83521)^{4} \)
(T + 83521)^4
$19$
\( T^{4} + 505964 T^{3} + \cdots + 32\!\cdots\!32 \)
T^4 + 505964*T^3 - 1163538994968*T^2 - 257353201425505024*T + 326820917830505177756032
$23$
\( T^{4} - 404838 T^{3} + \cdots + 93\!\cdots\!00 \)
T^4 - 404838*T^3 - 1121982566298*T^2 - 143860694317351200*T + 93769129730700728064000
$29$
\( T^{4} - 4590792 T^{3} + \cdots - 14\!\cdots\!00 \)
T^4 - 4590792*T^3 - 27804145231500*T^2 + 152369019715292604000*T - 148323112789718802844800000
$31$
\( T^{4} - 4952578 T^{3} + \cdots - 40\!\cdots\!00 \)
T^4 - 4952578*T^3 - 66433609550154*T^2 + 380821076479875228800*T - 402144835305961803710290400
$37$
\( T^{4} - 11290592 T^{3} + \cdots + 22\!\cdots\!96 \)
T^4 - 11290592*T^3 - 265881458407068*T^2 + 1688103931025136138688*T + 22051496533111017713349032896
$41$
\( T^{4} + 11496912 T^{3} + \cdots - 28\!\cdots\!60 \)
T^4 + 11496912*T^3 - 580925232087912*T^2 - 160296613041028919616*T - 2866196203770026966747760
$43$
\( T^{4} - 53686900 T^{3} + \cdots - 21\!\cdots\!80 \)
T^4 - 53686900*T^3 + 219664199195448*T^2 + 19671525510295274879936*T - 212385808552531637150364385280
$47$
\( T^{4} - 57601536 T^{3} + \cdots - 14\!\cdots\!00 \)
T^4 - 57601536*T^3 - 1045851838226736*T^2 + 106511329557781660385280*T - 1459998514793873044489214361600
$53$
\( T^{4} + 98104464 T^{3} + \cdots - 10\!\cdots\!88 \)
T^4 + 98104464*T^3 - 1996269824435928*T^2 - 227348334141147050143104*T - 1087138725165332755332140336688
$59$
\( T^{4} + 1116948 T^{3} + \cdots + 29\!\cdots\!00 \)
T^4 + 1116948*T^3 - 36660028311630600*T^2 + 257336968161206251800000*T + 298651280996619239323920480000000
$61$
\( T^{4} + 62897560 T^{3} + \cdots + 85\!\cdots\!92 \)
T^4 + 62897560*T^3 - 28573806204394956*T^2 - 885912197956929374334272*T + 85630387749002382683177495449792
$67$
\( T^{4} + 69022280 T^{3} + \cdots + 43\!\cdots\!16 \)
T^4 + 69022280*T^3 - 27329164479073008*T^2 + 703336469351706467089280*T + 4302279763437551847570617583616
$71$
\( T^{4} + 202453914 T^{3} + \cdots + 52\!\cdots\!00 \)
T^4 + 202453914*T^3 - 84651755022688050*T^2 - 14832606203121838881463200*T + 528946479139645630863930385152000
$73$
\( T^{4} - 312667256 T^{3} + \cdots + 13\!\cdots\!44 \)
T^4 - 312667256*T^3 - 9803507592357192*T^2 + 3799280514327905848109728*T + 136787754400040693948017598636944
$79$
\( T^{4} + 886063442 T^{3} + \cdots + 89\!\cdots\!16 \)
T^4 + 886063442*T^3 + 243424506331864374*T^2 + 25787253464003509697555168*T + 891938986079350778154828469599616
$83$
\( T^{4} + 1760033004 T^{3} + \cdots + 17\!\cdots\!00 \)
T^4 + 1760033004*T^3 + 1027150722379341048*T^2 + 232376169934803249505281600*T + 17586838675015533276228927477504000
$89$
\( T^{4} - 100343712 T^{3} + \cdots - 58\!\cdots\!00 \)
T^4 - 100343712*T^3 - 521070955191087252*T^2 - 144158701188827456752562064*T - 5868877601309558101674163742858400
$97$
\( T^{4} - 63193280 T^{3} + \cdots + 38\!\cdots\!52 \)
T^4 - 63193280*T^3 - 1367100569987946936*T^2 - 1212472857044533653499328*T + 387052828805422356819393582368367952
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