[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
\( T_{5}^{7} - 80 T_{5}^{6} - 10320 T_{5}^{5} + 635432 T_{5}^{4} + 38621312 T_{5}^{3} - 1023911424 T_{5}^{2} - 60024250368 T_{5} - 490461308928 \)
T5^7 - 80*T5^6 - 10320*T5^5 + 635432*T5^4 + 38621312*T5^3 - 1023911424*T5^2 - 60024250368*T5 - 490461308928
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(1104))\).
$p$
$F_p(T)$
$2$
\( T^{7} \)
T^7
$3$
\( (T - 9)^{7} \)
(T - 9)^7
$5$
\( T^{7} - 80 T^{6} + \cdots - 490461308928 \)
T^7 - 80*T^6 - 10320*T^5 + 635432*T^4 + 38621312*T^3 - 1023911424*T^2 - 60024250368*T - 490461308928
$7$
\( T^{7} + 46 T^{6} + \cdots + 1374810163200 \)
T^7 + 46*T^6 - 40532*T^5 - 2886080*T^4 + 188915440*T^3 + 10754423968*T^2 - 264732235200*T + 1374810163200
$11$
\( T^{7} + 124 T^{6} + \cdots - 27\!\cdots\!00 \)
T^7 + 124*T^6 - 1027912*T^5 - 82078368*T^4 + 274039477632*T^3 + 2739514203648*T^2 - 13275817561128960*T - 279460588946227200
$13$
\( T^{7} - 966 T^{6} + \cdots - 14\!\cdots\!20 \)
T^7 - 966*T^6 - 1355308*T^5 + 903050440*T^4 + 673301241392*T^3 - 115882841881376*T^2 - 110816273959212608*T - 14414610599583739520
$17$
\( T^{7} - 652 T^{6} + \cdots - 61\!\cdots\!72 \)
T^7 - 652*T^6 - 3629032*T^5 + 313013512*T^4 + 3233033107904*T^3 + 194737711844672*T^2 - 819382555361622528*T - 61529111512548867072
$19$
\( T^{7} - 542 T^{6} + \cdots + 29\!\cdots\!80 \)
T^7 - 542*T^6 - 4239276*T^5 + 3089151904*T^4 + 4129532156016*T^3 - 3926713987808352*T^2 + 194132104577014464*T + 292308784564837466880
$23$
\( (T + 529)^{7} \)
(T + 529)^7
$29$
\( T^{7} - 5222 T^{6} + \cdots - 14\!\cdots\!00 \)
T^7 - 5222*T^6 - 27633996*T^5 + 165391060104*T^4 + 78001771519280*T^3 - 1309407257997877024*T^2 + 1587245954760261124032*T - 144668563885384206480000
$31$
\( T^{7} - 2660 T^{6} + \cdots + 23\!\cdots\!60 \)
T^7 - 2660*T^6 - 67103856*T^5 + 48723917952*T^4 + 1023555371246336*T^3 - 571829198143114240*T^2 - 4179849035402660745216*T + 2327137400105313422376960
$37$
\( T^{7} + 202 T^{6} + \cdots + 21\!\cdots\!36 \)
T^7 + 202*T^6 - 298202564*T^5 + 1233030279096*T^4 + 22523596208800496*T^3 - 185195295985839133600*T^2 + 333939918921146277824576*T + 215443330423172859534020736
$41$
\( T^{7} + 706 T^{6} + \cdots + 16\!\cdots\!00 \)
T^7 + 706*T^6 - 551314124*T^5 + 1920316971368*T^4 + 85118209798324528*T^3 - 518468374006908019104*T^2 - 2469247473492456282515520*T + 16577957797066656842000457600
$43$
\( T^{7} - 7086 T^{6} + \cdots + 12\!\cdots\!00 \)
T^7 - 7086*T^6 - 541048732*T^5 + 4227916205248*T^4 + 79160228875821168*T^3 - 638667843356879279200*T^2 - 1947775835638125944193600*T + 12345211436794916309994528000
$47$
\( T^{7} - 37696 T^{6} + \cdots - 17\!\cdots\!00 \)
T^7 - 37696*T^6 - 185293904*T^5 + 23467148294144*T^4 - 309058155660197888*T^3 + 951846330003861635072*T^2 + 3783430248300621706100736*T - 17833192534570739510122905600
$53$
\( T^{7} - 30180 T^{6} + \cdots - 27\!\cdots\!92 \)
T^7 - 30180*T^6 - 1754428096*T^5 + 32950351080728*T^4 + 1346806759508767104*T^3 - 5745899080458687865856*T^2 - 409050582224375355273129984*T - 2783289010889062991281503854592
$59$
\( T^{7} - 12284 T^{6} + \cdots + 39\!\cdots\!00 \)
T^7 - 12284*T^6 - 1951265280*T^5 + 26255585900288*T^4 + 1238872906246353664*T^3 - 17894884483108740645888*T^2 - 255312912188542592844185600*T + 3907757301487637959000812748800
$61$
\( T^{7} - 53534 T^{6} + \cdots + 31\!\cdots\!00 \)
T^7 - 53534*T^6 - 1515013124*T^5 + 143093565815640*T^4 - 2585754928685196304*T^3 + 3402504657062057950432*T^2 + 151551450509051133906098240*T + 315496093588917634112435728000
$67$
\( T^{7} + 47750 T^{6} + \cdots - 12\!\cdots\!20 \)
T^7 + 47750*T^6 - 463682444*T^5 - 48973552251072*T^4 - 823898666255855632*T^3 - 5518699175801178173472*T^2 - 15175658934479184195039552*T - 12549779845634863462296510720
$71$
\( T^{7} - 2552 T^{6} + \cdots - 89\!\cdots\!60 \)
T^7 - 2552*T^6 - 8287706848*T^5 + 163375556539648*T^4 + 15303549145201936384*T^3 - 545492740373331608190976*T^2 + 5208065001929382555552841728*T - 8930321053907738735659985141760
$73$
\( T^{7} + 19474 T^{6} + \cdots + 23\!\cdots\!20 \)
T^7 + 19474*T^6 - 15090626156*T^5 - 118166471193368*T^4 + 75662720008546978864*T^3 - 412237721622392629743776*T^2 - 129000193075384820459286264384*T + 2381837937400051838552023038414720
$79$
\( T^{7} - 4510 T^{6} + \cdots - 14\!\cdots\!36 \)
T^7 - 4510*T^6 - 15513515300*T^5 - 209628648145440*T^4 + 66296883708970744304*T^3 + 1999726852337374484670048*T^2 - 41009104315748433512988543168*T - 1471060924408332886229205565211136
$83$
\( T^{7} - 47580 T^{6} + \cdots - 20\!\cdots\!00 \)
T^7 - 47580*T^6 - 11500244744*T^5 + 437502160108192*T^4 + 37898018569021904256*T^3 - 836039422436761060236800*T^2 - 32399130722827325892574003200*T - 207269945925198160175564304384000
$89$
\( T^{7} - 150664 T^{6} + \cdots - 24\!\cdots\!40 \)
T^7 - 150664*T^6 - 3306543768*T^5 + 1234784774774552*T^4 - 33018010175977990208*T^3 - 757690024679567648871744*T^2 + 9467287589911700599334148096*T - 24774005590400709126109309040640
$97$
\( T^{7} - 392426 T^{6} + \cdots + 61\!\cdots\!88 \)
T^7 - 392426*T^6 + 43550531252*T^5 + 293813113743416*T^4 - 255141677665139095248*T^3 + 5780999692977698202142752*T^2 + 215860268357570738772630728640*T + 615838826660102857306902813775488
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