[N,k,chi] = [546,8,Mod(1,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.1");
S:= CuspForms(chi, 8);
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
\(2\)
\(1\)
\(3\)
\(1\)
\(7\)
\(1\)
\(13\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{6} + 35T_{5}^{5} - 279647T_{5}^{4} + 16831477T_{5}^{3} + 13486311926T_{5}^{2} - 985141562480T_{5} - 101419644337200 \)
T5^6 + 35*T5^5 - 279647*T5^4 + 16831477*T5^3 + 13486311926*T5^2 - 985141562480*T5 - 101419644337200
acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(546))\).
$p$
$F_p(T)$
$2$
\( (T + 8)^{6} \)
(T + 8)^6
$3$
\( (T + 27)^{6} \)
(T + 27)^6
$5$
\( T^{6} + \cdots - 101419644337200 \)
T^6 + 35*T^5 - 279647*T^4 + 16831477*T^3 + 13486311926*T^2 - 985141562480*T - 101419644337200
$7$
\( (T + 343)^{6} \)
(T + 343)^6
$11$
\( T^{6} - 5606 T^{5} + \cdots - 12\!\cdots\!52 \)
T^6 - 5606*T^5 - 36061733*T^4 + 131789837558*T^3 + 509554734839828*T^2 - 319518970670823496*T - 1210332022076083390752
$13$
\( (T + 2197)^{6} \)
(T + 2197)^6
$17$
\( T^{6} - 22022 T^{5} + \cdots - 60\!\cdots\!12 \)
T^6 - 22022*T^5 - 2464812773*T^4 + 40078039859910*T^3 + 2056491010931649612*T^2 - 17649009992333316293640*T - 602574964630961654264133312
$19$
\( T^{6} + 5779 T^{5} + \cdots + 10\!\cdots\!08 \)
T^6 + 5779*T^5 - 2784626393*T^4 - 31236275276247*T^3 + 785312885822736660*T^2 - 1881209380412914387776*T + 1061888083834608212894208
$23$
\( T^{6} + 110789 T^{5} + \cdots + 26\!\cdots\!16 \)
T^6 + 110789*T^5 + 1617105595*T^4 - 69476278007957*T^3 - 263791577270782612*T^2 + 5685494783836080021880*T + 26992557184371815142575616
$29$
\( T^{6} - 30693 T^{5} + \cdots - 91\!\cdots\!72 \)
T^6 - 30693*T^5 - 60295531315*T^4 + 2319626939050969*T^3 + 688105797641211507546*T^2 - 2339430712379273129665060*T - 910487259957230351073418909272
$31$
\( T^{6} - 180467 T^{5} + \cdots - 36\!\cdots\!08 \)
T^6 - 180467*T^5 - 82579241564*T^4 + 9908292044855312*T^3 + 1702528993900096528832*T^2 - 40282141980646363849951744*T - 3668730871707292427398315819008
$37$
\( T^{6} + 322222 T^{5} + \cdots + 27\!\cdots\!84 \)
T^6 + 322222*T^5 - 194400244769*T^4 - 70772549327531106*T^3 + 5359081146831079505556*T^2 + 3490967023832132007645717288*T + 270798760774796397000824937446784
$41$
\( T^{6} + 212652 T^{5} + \cdots + 68\!\cdots\!24 \)
T^6 + 212652*T^5 - 660500315956*T^4 - 62397517695109728*T^3 + 81232390830675202320864*T^2 + 14217487991638983334323897984*T + 68383607639256958066233425409024
$43$
\( T^{6} + 329299 T^{5} + \cdots + 10\!\cdots\!88 \)
T^6 + 329299*T^5 - 870381817789*T^4 - 347606548905922955*T^3 + 143999837131171947141860*T^2 + 84491544208833994478722855120*T + 10072243227981498663606458265364288
$47$
\( T^{6} - 1322861 T^{5} + \cdots + 17\!\cdots\!80 \)
T^6 - 1322861*T^5 - 802664774324*T^4 + 1714436810794532156*T^3 - 622314501886700266224784*T^2 - 6817799293672868165575880704*T + 17809697588987970271124029032775680
$53$
\( T^{6} + 168719 T^{5} + \cdots + 21\!\cdots\!60 \)
T^6 + 168719*T^5 - 4054076878974*T^4 - 56306444825448600*T^3 + 3375992139000449192937216*T^2 - 1623861116972457516578316787344*T + 212195335189033405199091539554630560
$59$
\( T^{6} - 1943712 T^{5} + \cdots - 10\!\cdots\!36 \)
T^6 - 1943712*T^5 - 8902084778284*T^4 + 10089009910190218480*T^3 + 25167482857722153130795200*T^2 - 4548055489892739905998382483200*T - 10420810612803563208924652709793140736
$61$
\( T^{6} + 1085922 T^{5} + \cdots - 21\!\cdots\!40 \)
T^6 + 1085922*T^5 - 14274127564215*T^4 - 6361818756027728252*T^3 + 53438167028439856633453632*T^2 - 11136496200103775935503031834416*T - 212447210407696659720651027119065040
$67$
\( T^{6} - 885066 T^{5} + \cdots - 48\!\cdots\!76 \)
T^6 - 885066*T^5 - 13665964903396*T^4 + 4256993414876023208*T^3 + 47937867124181909425452480*T^2 - 4707752485119823161854507815808*T - 48093432118784397494420827001366731776
$71$
\( T^{6} - 1626164 T^{5} + \cdots - 35\!\cdots\!04 \)
T^6 - 1626164*T^5 - 24160723526876*T^4 + 68584864468938195344*T^3 - 67142117088677021488234048*T^2 + 26868836587506384942812328495872*T - 3510683709016939647425026700792008704
$73$
\( T^{6} + 4750115 T^{5} + \cdots - 99\!\cdots\!32 \)
T^6 + 4750115*T^5 - 3533688010823*T^4 - 28925941581985379879*T^3 + 7046060977460747701435910*T^2 + 38698183427955966963357045959164*T - 9968808000809817141508963129979487432
$79$
\( T^{6} - 1794289 T^{5} + \cdots - 14\!\cdots\!24 \)
T^6 - 1794289*T^5 - 99079884638216*T^4 + 137205455370334372876*T^3 + 2740070981472774567286294976*T^2 - 2380000803884139536574268241350016*T - 14896768306132569112652950903649794458624
$83$
\( T^{6} + 8454255 T^{5} + \cdots + 16\!\cdots\!76 \)
T^6 + 8454255*T^5 - 88511013171976*T^4 - 814449324347084639184*T^3 + 1459433228279598018888067296*T^2 + 18577911786715355912409434138813520*T + 16176351628398947745543270588707005584576
$89$
\( T^{6} + 6055411 T^{5} + \cdots - 94\!\cdots\!48 \)
T^6 + 6055411*T^5 - 55163501976282*T^4 - 35123537228743346412*T^3 + 464595227837025648503083848*T^2 - 31384542048301174163479788862080*T - 948274012704262487115343478937862016448
$97$
\( T^{6} + 9823899 T^{5} + \cdots + 11\!\cdots\!84 \)
T^6 + 9823899*T^5 - 115678965662938*T^4 - 776355091749381953960*T^3 + 3529216111725862306908947712*T^2 + 11724843992047252865190441917607152*T + 1111350526444291409470604327018046789984
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