[N,k,chi] = [1104,6,Mod(1,1104)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1104, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1104.1");
S:= CuspForms(chi, 6);
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
\( T_{5}^{6} - 42T_{5}^{5} - 6244T_{5}^{4} + 245184T_{5}^{3} + 4855680T_{5}^{2} - 171131392T_{5} + 590425088 \)
T5^6 - 42*T5^5 - 6244*T5^4 + 245184*T5^3 + 4855680*T5^2 - 171131392*T5 + 590425088
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(1104))\).
$p$
$F_p(T)$
$2$
\( T^{6} \)
T^6
$3$
\( (T - 9)^{6} \)
(T - 9)^6
$5$
\( T^{6} - 42 T^{5} + \cdots + 590425088 \)
T^6 - 42*T^5 - 6244*T^4 + 245184*T^3 + 4855680*T^2 - 171131392*T + 590425088
$7$
\( T^{6} - 82 T^{5} + \cdots - 10211152303168 \)
T^6 - 82*T^5 - 84732*T^4 + 5735520*T^3 + 1748745136*T^2 - 65522508000*T - 10211152303168
$11$
\( T^{6} + \cdots - 617873698758656 \)
T^6 + 560*T^5 - 359272*T^4 - 128427776*T^3 + 46608985984*T^2 + 532806486016*T - 617873698758656
$13$
\( T^{6} + 1800 T^{5} + \cdots + 13\!\cdots\!04 \)
T^6 + 1800*T^5 + 400644*T^4 - 580482432*T^3 - 182558545104*T^2 + 50009535676800*T + 13392245282458304
$17$
\( T^{6} + 118 T^{5} + \cdots - 21\!\cdots\!24 \)
T^6 + 118*T^5 - 6089060*T^4 + 1595911024*T^3 + 9095962589984*T^2 - 3588265110191104*T - 2156294722098497024
$19$
\( T^{6} + 1326 T^{5} + \cdots - 53\!\cdots\!00 \)
T^6 + 1326*T^5 - 13348252*T^4 - 14411279984*T^3 + 52310044100976*T^2 + 36758835121183200*T - 53045794088220571200
$23$
\( (T + 529)^{6} \)
(T + 529)^6
$29$
\( T^{6} - 9440 T^{5} + \cdots - 66\!\cdots\!76 \)
T^6 - 9440*T^5 - 3310060*T^4 + 117406575936*T^3 + 115585609877936*T^2 - 63748853776941824*T - 66518325100031987776
$31$
\( T^{6} - 7132 T^{5} + \cdots - 19\!\cdots\!28 \)
T^6 - 7132*T^5 - 53507376*T^4 + 292491298048*T^3 + 733663166138112*T^2 - 913275705681773568*T - 1912539114948714467328
$37$
\( T^{6} - 8168 T^{5} + \cdots - 69\!\cdots\!72 \)
T^6 - 8168*T^5 - 160430804*T^4 + 1184576316576*T^3 + 7106734477446832*T^2 - 40411277377455762944*T - 69472833516351601435072
$41$
\( T^{6} - 5012 T^{5} + \cdots + 55\!\cdots\!28 \)
T^6 - 5012*T^5 - 473373204*T^4 - 430326085600*T^3 + 59192155981606512*T^2 + 370284228709235819712*T + 555425791789103450296128
$43$
\( T^{6} - 14762 T^{5} + \cdots + 45\!\cdots\!32 \)
T^6 - 14762*T^5 - 189791356*T^4 + 4158567252624*T^3 - 18285450100482448*T^2 - 666246939542679200*T + 45152552131661323063232
$47$
\( T^{6} + 15904 T^{5} + \cdots + 11\!\cdots\!12 \)
T^6 + 15904*T^5 - 191365072*T^4 - 2508295737856*T^3 + 5979547170224128*T^2 + 87274257294144929792*T + 112944545265177471680512
$53$
\( T^{6} - 58414 T^{5} + \cdots - 43\!\cdots\!08 \)
T^6 - 58414*T^5 + 351103668*T^4 + 26287884484096*T^3 - 312442334212396416*T^2 - 797334824043891726336*T - 433150540336445852049408
$59$
\( T^{6} - 38640 T^{5} + \cdots + 72\!\cdots\!00 \)
T^6 - 38640*T^5 + 137472512*T^4 + 3982806267904*T^3 - 10447766804022528*T^2 - 90026852830801510400*T + 72107134668270016921600
$61$
\( T^{6} - 25192 T^{5} + \cdots + 13\!\cdots\!52 \)
T^6 - 25192*T^5 - 666970196*T^4 + 22275628474784*T^3 - 60093358907383120*T^2 - 2231555973502364602880*T + 13795444754983434731877952
$67$
\( T^{6} - 50446 T^{5} + \cdots + 14\!\cdots\!24 \)
T^6 - 50446*T^5 - 4192642348*T^4 + 212756302500784*T^3 + 3622291276786186480*T^2 - 227234675149105404188384*T + 1483382459732981960400658624
$71$
\( T^{6} - 8464 T^{5} + \cdots - 23\!\cdots\!00 \)
T^6 - 8464*T^5 - 7195385696*T^4 - 18987523084288*T^3 + 11117349927408748544*T^2 + 109716683998431197593600*T - 2312292974349343282311987200
$73$
\( T^{6} + 63132 T^{5} + \cdots + 10\!\cdots\!68 \)
T^6 + 63132*T^5 - 3790587348*T^4 - 345883038709856*T^3 - 6378457034408756112*T^2 + 24040836862150133767104*T + 1038342776659276987663426368
$79$
\( T^{6} - 239558 T^{5} + \cdots - 12\!\cdots\!28 \)
T^6 - 239558*T^5 + 14085216740*T^4 + 691469337713440*T^3 - 97537151945922860880*T^2 + 2851110977935814078647392*T - 12042956498951432520663064128
$83$
\( T^{6} - 120464 T^{5} + \cdots + 39\!\cdots\!36 \)
T^6 - 120464*T^5 - 6501844520*T^4 + 1142407672636160*T^3 - 22913565289037885568*T^2 - 591919341498956328376320*T + 3953760858298836153482305536
$89$
\( T^{6} + 33298 T^{5} + \cdots - 15\!\cdots\!24 \)
T^6 + 33298*T^5 - 36920916652*T^4 - 988254725092080*T^3 + 431736776288853241184*T^2 + 7384465852660801512845824*T - 1550524135070346754399992884224
$97$
\( T^{6} - 92376 T^{5} + \cdots + 48\!\cdots\!76 \)
T^6 - 92376*T^5 - 8985604828*T^4 + 456380761730944*T^3 + 4791469523898015024*T^2 - 186208821794844404309120*T + 488699634372673817967222976
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