[N,k,chi] = [567,4,Mod(1,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.1");
S:= CuspForms(chi, 4);
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
\(3\)
\(-1\)
\(7\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{8} + 3T_{2}^{7} - 49T_{2}^{6} - 138T_{2}^{5} + 708T_{2}^{4} + 1941T_{2}^{3} - 2506T_{2}^{2} - 8592T_{2} - 4616 \)
T2^8 + 3*T2^7 - 49*T2^6 - 138*T2^5 + 708*T2^4 + 1941*T2^3 - 2506*T2^2 - 8592*T2 - 4616
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(567))\).
$p$
$F_p(T)$
$2$
\( T^{8} + 3 T^{7} - 49 T^{6} + \cdots - 4616 \)
T^8 + 3*T^7 - 49*T^6 - 138*T^5 + 708*T^4 + 1941*T^3 - 2506*T^2 - 8592*T - 4616
$3$
\( T^{8} \)
T^8
$5$
\( T^{8} + 30 T^{7} - 172 T^{6} + \cdots - 5370473 \)
T^8 + 30*T^7 - 172*T^6 - 8610*T^5 + 14001*T^4 + 565608*T^3 - 3397711*T^2 + 7233858*T - 5370473
$7$
\( (T + 7)^{8} \)
(T + 7)^8
$11$
\( T^{8} + 24 T^{7} + \cdots + 4399098628 \)
T^8 + 24*T^7 - 3760*T^6 - 84834*T^5 + 3617979*T^4 + 64097388*T^3 - 820937803*T^2 - 8149275276*T + 4399098628
$13$
\( T^{8} - 68 T^{7} + \cdots - 8057410599908 \)
T^8 - 68*T^7 - 6887*T^6 + 584044*T^5 + 3974167*T^4 - 1046864588*T^3 + 11935027315*T^2 + 466823643556*T - 8057410599908
$17$
\( T^{8} + 168 T^{7} + \cdots + 2073513126204 \)
T^8 + 168*T^7 - 8910*T^6 - 2480508*T^5 - 32700159*T^4 + 8466840468*T^3 + 250373208411*T^2 - 1554538753260*T + 2073513126204
$19$
\( T^{8} + \cdots - 604815137888177 \)
T^8 - 176*T^7 - 12980*T^6 + 3616846*T^5 - 63882233*T^4 - 15172506716*T^3 + 473899377403*T^2 + 18413307722920*T - 604815137888177
$23$
\( T^{8} + \cdots - 145237005548415 \)
T^8 + 228*T^7 - 19827*T^6 - 6216822*T^5 - 89682147*T^4 + 22928842098*T^3 + 426462975270*T^2 - 15365757330018*T - 145237005548415
$29$
\( T^{8} + \cdots + 498541969683460 \)
T^8 + 618*T^7 + 108797*T^6 - 218022*T^5 - 1333718022*T^4 - 42151101756*T^3 + 4126180974341*T^2 + 111593220428004*T + 498541969683460
$31$
\( T^{8} - 72 T^{7} + \cdots - 21\!\cdots\!92 \)
T^8 - 72*T^7 - 110799*T^6 + 4044006*T^5 + 3419732898*T^4 - 17995301658*T^3 - 29397434125473*T^2 - 865622373907284*T - 2141134930990692
$37$
\( T^{8} - 210 T^{7} + \cdots + 71\!\cdots\!88 \)
T^8 - 210*T^7 - 131643*T^6 + 12199410*T^5 + 6138784098*T^4 + 124534542204*T^3 - 52771182253767*T^2 - 1595546991527796*T + 71324346320230788
$41$
\( T^{8} + 420 T^{7} + \cdots + 46\!\cdots\!36 \)
T^8 + 420*T^7 - 87130*T^6 - 49443456*T^5 - 128239347*T^4 + 1199664512340*T^3 - 6676629991213*T^2 - 10682988414253200*T + 462426168557412736
$43$
\( T^{8} + 2 T^{7} + \cdots + 20\!\cdots\!84 \)
T^8 + 2*T^7 - 461129*T^6 - 10001572*T^5 + 67028138194*T^4 + 1857073655618*T^3 - 3087591835842791*T^2 - 18965485935823156*T + 20950193983088735284
$47$
\( T^{8} + 570 T^{7} + \cdots - 26\!\cdots\!96 \)
T^8 + 570*T^7 - 1665*T^6 - 43446078*T^5 - 3679740576*T^4 + 849034787274*T^3 + 72863146602747*T^2 - 3690234827458704*T - 266172075699679296
$53$
\( T^{8} + 528 T^{7} + \cdots + 86\!\cdots\!08 \)
T^8 + 528*T^7 - 587934*T^6 - 437892894*T^5 + 17633836809*T^4 + 81691443067554*T^3 + 24282335794603149*T^2 + 2650393862685934092*T + 86158340642449528308
$59$
\( T^{8} - 150 T^{7} + \cdots + 34\!\cdots\!52 \)
T^8 - 150*T^7 - 674415*T^6 + 42907140*T^5 + 134276268996*T^4 + 3568497587424*T^3 - 7516085639118957*T^2 - 800025206240455272*T + 3497507042491117152
$61$
\( T^{8} - 578 T^{7} + \cdots + 79\!\cdots\!35 \)
T^8 - 578*T^7 - 336029*T^6 + 239974072*T^5 - 24959688881*T^4 - 3900655026314*T^3 + 265758786651520*T^2 + 34334165070805642*T + 797499529610837935
$67$
\( T^{8} + 898 T^{7} + \cdots + 16\!\cdots\!68 \)
T^8 + 898*T^7 - 808250*T^6 - 649638344*T^5 + 159691772083*T^4 + 110804701702978*T^3 - 4376198717597015*T^2 - 4042724170048486616*T + 16406775796815316768
$71$
\( T^{8} + 882 T^{7} + \cdots + 36\!\cdots\!25 \)
T^8 + 882*T^7 - 1297368*T^6 - 1037538936*T^5 + 541546496631*T^4 + 370893752864550*T^3 - 84625618285280943*T^2 - 41762863933845347934*T + 3615433389655081652925
$73$
\( T^{8} - 972 T^{7} + \cdots + 45\!\cdots\!76 \)
T^8 - 972*T^7 - 1393785*T^6 + 1566589032*T^5 + 98139802230*T^4 - 334588931457660*T^3 + 7761474434502279*T^2 + 20102375258878654764*T + 459207760252279618476
$79$
\( T^{8} + 158 T^{7} + \cdots + 13\!\cdots\!09 \)
T^8 + 158*T^7 - 2287370*T^6 - 251111914*T^5 + 1655367536629*T^4 + 137375639612150*T^3 - 396022336235969075*T^2 - 36002589298497772636*T + 13560397108002123496009
$83$
\( T^{8} + 2958 T^{7} + \cdots - 13\!\cdots\!60 \)
T^8 + 2958*T^7 + 2129274*T^6 - 1328931702*T^5 - 2454567763617*T^4 - 1160957901101148*T^3 - 213297172017370389*T^2 - 12507738718368381408*T - 139674885225712871760
$89$
\( T^{8} + 4380 T^{7} + \cdots + 44\!\cdots\!84 \)
T^8 + 4380*T^7 + 5183942*T^6 - 1699594764*T^5 - 5942862637383*T^4 - 1461374513042748*T^3 + 1426979281925511527*T^2 + 565461385519812405432*T + 44071100134958216322784
$97$
\( T^{8} + 60 T^{7} + \cdots - 22\!\cdots\!00 \)
T^8 + 60*T^7 - 4188249*T^6 + 1124173728*T^5 + 4347204763950*T^4 - 2329113227232420*T^3 - 75028456400690025*T^2 + 190113418932003897228*T - 22111705142683651502100
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