[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
\( T_{5}^{6} - 13T_{5}^{5} - 366951T_{5}^{4} - 14766175T_{5}^{3} + 34912599250T_{5}^{2} + 1283526912000T_{5} - 936578573280000 \)
T5^6 - 13*T5^5 - 366951*T5^4 - 14766175*T5^3 + 34912599250*T5^2 + 1283526912000*T5 - 936578573280000
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
$5$
\( T^{6} + \cdots - 936578573280000 \)
T^6 - 13*T^5 - 366951*T^4 - 14766175*T^3 + 34912599250*T^2 + 1283526912000*T - 936578573280000
$7$
\( (T - 343)^{6} \)
(T - 343)^6
$11$
\( T^{6} - 10054 T^{5} + \cdots + 16\!\cdots\!68 \)
T^6 - 10054*T^5 - 44295597*T^4 + 673184547830*T^3 - 917226338618324*T^2 - 6781412275063368024*T + 16260921237206632039968
$13$
\( (T + 2197)^{6} \)
(T + 2197)^6
$17$
\( T^{6} - 21222 T^{5} + \cdots - 16\!\cdots\!28 \)
T^6 - 21222*T^5 - 1479057917*T^4 + 28878282570126*T^3 + 266140678897465804*T^2 - 2759503594273546137864*T - 16547702833655725404068928
$19$
\( T^{6} - 9527 T^{5} + \cdots - 16\!\cdots\!64 \)
T^6 - 9527*T^5 - 1876151505*T^4 - 3025888088429*T^3 + 473325456102939028*T^2 - 2414469081180217424544*T - 1649977096599622411764864
$23$
\( T^{6} - 33229 T^{5} + \cdots - 34\!\cdots\!52 \)
T^6 - 33229*T^5 - 10546427729*T^4 + 246832081463217*T^3 + 34413281424804396540*T^2 - 421496708494015938677400*T - 34754127185282388054250457952
$29$
\( T^{6} - 174185 T^{5} + \cdots + 92\!\cdots\!32 \)
T^6 - 174185*T^5 - 35578686587*T^4 + 5589489051926901*T^3 + 174189061240655479914*T^2 - 36383803365530813310242964*T + 927336694389148161559637091432
$31$
\( T^{6} - 119045 T^{5} + \cdots - 77\!\cdots\!80 \)
T^6 - 119045*T^5 - 130082373580*T^4 + 18744313478857840*T^3 + 3620998095933108320576*T^2 - 519474607103199379197483008*T - 7740817610353026026692749946880
$37$
\( T^{6} - 56562 T^{5} + \cdots + 43\!\cdots\!72 \)
T^6 - 56562*T^5 - 239344024977*T^4 + 48750536762135446*T^3 + 2531000800465976691204*T^2 - 948508610004131815128315384*T + 43360930524748767963038626718272
$41$
\( T^{6} - 101632 T^{5} + \cdots + 37\!\cdots\!08 \)
T^6 - 101632*T^5 - 305083615196*T^4 - 12655318554577296*T^3 + 18501182762907988738944*T^2 + 1810325107475664741345139200*T + 37062690700971502951135252881408
$43$
\( T^{6} - 441323 T^{5} + \cdots + 26\!\cdots\!00 \)
T^6 - 441323*T^5 - 534916915253*T^4 + 46555280885979651*T^3 + 63592022962481437508988*T^2 + 7849085308857599585166445680*T + 265211471819541914039981386756800
$47$
\( T^{6} + 892849 T^{5} + \cdots + 70\!\cdots\!52 \)
T^6 + 892849*T^5 - 661748750880*T^4 - 592637865945161540*T^3 + 82487347885572856817536*T^2 + 91432687413906333031170527232*T + 7040967959565318120200210289917952
$53$
\( T^{6} - 2093965 T^{5} + \cdots + 27\!\cdots\!16 \)
T^6 - 2093965*T^5 - 3525714964198*T^4 + 10163463538020989000*T^3 - 2800938967651030902816448*T^2 - 5623459918662045165997173586000*T + 2733049013459264003598704142818019616
$59$
\( T^{6} + 136204 T^{5} + \cdots + 46\!\cdots\!20 \)
T^6 + 136204*T^5 - 2045540977236*T^4 - 867547726719102176*T^3 + 476074623512502977569024*T^2 + 321138052958819164783823542272*T + 46401345390746948711670415911813120
$61$
\( T^{6} + 3989946 T^{5} + \cdots + 11\!\cdots\!20 \)
T^6 + 3989946*T^5 + 2562905696353*T^4 - 6019297950964593180*T^3 - 6727140593038436854021760*T^2 + 69856004009063555512671549648*T + 1124700242964133983312014001306828720
$67$
\( T^{6} + 2218250 T^{5} + \cdots - 48\!\cdots\!88 \)
T^6 + 2218250*T^5 - 10526998733956*T^4 - 13217009450631469192*T^3 + 30050111287663532369719040*T^2 + 11909508910254391518176996048768*T - 4812281086477737774748653818392844288
$71$
\( T^{6} - 2045928 T^{5} + \cdots - 22\!\cdots\!20 \)
T^6 - 2045928*T^5 - 21214227615948*T^4 + 36951832557596946672*T^3 + 132681560662489404006997632*T^2 - 162298561757013618242675785592832*T - 223026804971822274429520812394225336320
$73$
\( T^{6} + 8557479 T^{5} + \cdots + 47\!\cdots\!08 \)
T^6 + 8557479*T^5 + 6201131400745*T^4 - 74653362397933764459*T^3 - 122254568278622176958294138*T^2 + 9539307079193848653546620028972*T + 47780522333414316891218518409223708408
$79$
\( T^{6} + 8559709 T^{5} + \cdots + 36\!\cdots\!00 \)
T^6 + 8559709*T^5 - 26957447904664*T^4 - 308725665140783404604*T^3 - 74178446337027090851737024*T^2 + 2558386758663904280917064075814400*T + 3644213264224206103536634218967843840000
$83$
\( T^{6} - 2496351 T^{5} + \cdots - 54\!\cdots\!48 \)
T^6 - 2496351*T^5 - 28577962635596*T^4 + 31631712053415657768*T^3 + 229310739082276429184061952*T^2 - 103277302395500522102500364597808*T - 544957193368376459771978917038669790848
$89$
\( T^{6} + 2446683 T^{5} + \cdots + 20\!\cdots\!96 \)
T^6 + 2446683*T^5 - 81258529369598*T^4 - 202127972775831716172*T^3 + 82975059258270800991945352*T^2 + 69186952429500269653630856460288*T + 2002276765129195300230772033701741696
$97$
\( T^{6} - 5786889 T^{5} + \cdots - 28\!\cdots\!84 \)
T^6 - 5786889*T^5 - 284102796212738*T^4 + 437498702709074976792*T^3 + 19470437867119133562409613056*T^2 + 7518159031838983228893233895796272*T - 280523392831890690825733103836871202045984
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