[N,k,chi] = [153,10,Mod(1,153)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(153, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("153.1");
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
\(3\)
\(-1\)
\(17\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{5} - 33T_{2}^{4} - 1162T_{2}^{3} + 24920T_{2}^{2} + 344192T_{2} - 457728 \)
T2^5 - 33*T2^4 - 1162*T2^3 + 24920*T2^2 + 344192*T2 - 457728
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(153))\).
$p$
$F_p(T)$
$2$
\( T^{5} - 33 T^{4} - 1162 T^{3} + \cdots - 457728 \)
T^5 - 33*T^4 - 1162*T^3 + 24920*T^2 + 344192*T - 457728
$3$
\( T^{5} \)
T^5
$5$
\( T^{5} + 1480 T^{4} + \cdots + 60\!\cdots\!20 \)
T^5 + 1480*T^4 - 5422732*T^3 - 5931144800*T^2 + 6910711315456*T + 6073215799787520
$7$
\( T^{5} + 13202 T^{4} + \cdots - 26\!\cdots\!44 \)
T^5 + 13202*T^4 - 7845586*T^3 - 392836554656*T^2 - 769174397227488*T - 266210160692281344
$11$
\( T^{5} - 68036 T^{4} + \cdots - 18\!\cdots\!36 \)
T^5 - 68036*T^4 + 161240150*T^3 + 51654458131068*T^2 - 583150347803390760*T - 1830017988582058514736
$13$
\( T^{5} + 158862 T^{4} + \cdots + 46\!\cdots\!08 \)
T^5 + 158862*T^4 - 8325650340*T^3 - 1715294166968552*T^2 + 15605144350350783296*T + 4676449765506104481804608
$17$
\( (T - 83521)^{5} \)
(T - 83521)^5
$19$
\( T^{5} + 370992 T^{4} + \cdots - 23\!\cdots\!16 \)
T^5 + 370992*T^4 - 413150145000*T^3 - 176324676443571104*T^2 - 1723473673480067416704*T - 2312268047433447890351616
$23$
\( T^{5} + 1645870 T^{4} + \cdots - 28\!\cdots\!00 \)
T^5 + 1645870*T^4 - 2266461594322*T^3 - 4397519995817681960*T^2 - 1317519869881634606832896*T - 28288624760484633425673830400
$29$
\( T^{5} + 3668616 T^{4} + \cdots - 14\!\cdots\!00 \)
T^5 + 3668616*T^4 - 8671259026316*T^3 - 43135444415107067232*T^2 - 47323615841213371223933952*T - 14173986848343717908587629772800
$31$
\( T^{5} + 7262362 T^{4} + \cdots - 63\!\cdots\!72 \)
T^5 + 7262362*T^4 - 55088066425306*T^3 - 614282831765938150512*T^2 - 1536199628075135028581656416*T - 632058012044847300816113497699072
$37$
\( T^{5} + 31420708 T^{4} + \cdots + 12\!\cdots\!48 \)
T^5 + 31420708*T^4 + 352949672725220*T^3 + 1695567673557419157840*T^2 + 3175498108953277525618580160*T + 1205230962177583458197012210478848
$41$
\( T^{5} - 7996938 T^{4} + \cdots - 84\!\cdots\!52 \)
T^5 - 7996938*T^4 - 944595954515528*T^3 + 3447959195713599655632*T^2 + 165380302133326231165628431632*T - 846981083798239147774657062832865952
$43$
\( T^{5} + 56908268 T^{4} + \cdots - 35\!\cdots\!88 \)
T^5 + 56908268*T^4 + 104989881324440*T^3 - 42021924248871471304064*T^2 - 766454399851662299280273449472*T - 3576749165248389621523535121990156288
$47$
\( T^{5} - 16903336 T^{4} + \cdots + 53\!\cdots\!68 \)
T^5 - 16903336*T^4 - 2082901585389616*T^3 - 13688312901626222073984*T^2 + 133953896242418750141517139968*T + 539748137865083633117250354432442368
$53$
\( T^{5} - 83362982 T^{4} + \cdots - 46\!\cdots\!44 \)
T^5 - 83362982*T^4 - 9379424557396600*T^3 + 922691814745053279257616*T^2 - 15856574433788456469775189356336*T - 46867125504607368778641605770075928544
$59$
\( T^{5} - 37946604 T^{4} + \cdots - 43\!\cdots\!28 \)
T^5 - 37946604*T^4 - 31008104213596424*T^3 + 2321883840321235340294592*T^2 + 40295348770123095921148617603072*T - 4356544940660528194691504633190091849728
$61$
\( T^{5} + 77685452 T^{4} + \cdots - 81\!\cdots\!20 \)
T^5 + 77685452*T^4 - 33463527209865196*T^3 - 362977973708409911187632*T^2 + 246565101932082674932390414073792*T - 8101883624360069885067403534167838193920
$67$
\( T^{5} + 304503600 T^{4} + \cdots - 17\!\cdots\!00 \)
T^5 + 304503600*T^4 + 7020713481287504*T^3 - 5546744096762225125067776*T^2 - 589781236259965607097490571811840*T - 17235329736094640314087528932096655769600
$71$
\( T^{5} - 476602922 T^{4} + \cdots - 27\!\cdots\!64 \)
T^5 - 476602922*T^4 + 9603673423875238*T^3 + 14148910316839997808239784*T^2 - 344441007158719229321818957270528*T - 27765412759705741266271442198993949425664
$73$
\( T^{5} + 289980486 T^{4} + \cdots + 39\!\cdots\!92 \)
T^5 + 289980486*T^4 - 108975991091496536*T^3 - 24752992738947808147857616*T^2 + 1840776003312578849931641699419728*T + 393650956344854331563371211131778841453792
$79$
\( T^{5} + 828240610 T^{4} + \cdots + 88\!\cdots\!72 \)
T^5 + 828240610*T^4 + 104201235865665870*T^3 - 47567680186009725901976040*T^2 - 6009633729762284070745182120150144*T + 882271437547674419135925164648391276790272
$83$
\( T^{5} + 194681148 T^{4} + \cdots + 48\!\cdots\!16 \)
T^5 + 194681148*T^4 - 285056400431908168*T^3 - 93790244359764813711366208*T^2 - 3201194754950529740709532426224640*T + 482998206542120987178756180832780343279616
$89$
\( T^{5} + 376848106 T^{4} + \cdots - 26\!\cdots\!96 \)
T^5 + 376848106*T^4 - 834395900612571220*T^3 - 278290842908929725848832824*T^2 + 21299141259306618195796659676304128*T - 261476045726080651653452898155869833016896
$97$
\( T^{5} - 692035246 T^{4} + \cdots + 10\!\cdots\!28 \)
T^5 - 692035246*T^4 - 3215802378794508088*T^3 + 495879090336309987062891344*T^2 + 3027229362146948015650251958046641616*T + 1006410355936108669449825182902911948321357728
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