[N,k,chi] = [5,18,Mod(1,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.1");
S:= CuspForms(chi, 18);
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
\(5\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} - 118T_{2}^{2} - 198104T_{2} - 8070528 \)
T2^3 - 118*T2^2 - 198104*T2 - 8070528
acting on \(S_{18}^{\mathrm{new}}(\Gamma_0(5))\).
$p$
$F_p(T)$
$2$
\( T^{3} - 118 T^{2} - 198104 T - 8070528 \)
T^3 - 118*T^2 - 198104*T - 8070528
$3$
\( T^{3} - 15944 T^{2} + \cdots + 2578483943424 \)
T^3 - 15944*T^2 - 228550896*T + 2578483943424
$5$
\( (T - 390625)^{3} \)
(T - 390625)^3
$7$
\( T^{3} - 2139308 T^{2} + \cdots + 55\!\cdots\!12 \)
T^3 - 2139308*T^2 - 152997034923264*T + 556045487854496301312
$11$
\( T^{3} - 1789747516 T^{2} + \cdots - 25\!\cdots\!48 \)
T^3 - 1789747516*T^2 + 811652972530976752*T - 25750631040241724690576448
$13$
\( T^{3} - 5414696794 T^{2} + \cdots - 13\!\cdots\!36 \)
T^3 - 5414696794*T^2 + 5118982943993820044*T - 1341031629791996599005084536
$17$
\( T^{3} + 27402303962 T^{2} + \cdots + 37\!\cdots\!92 \)
T^3 + 27402303962*T^2 - 948325152327203501684*T + 374324630165366720823512892792
$19$
\( T^{3} + 29956565300 T^{2} + \cdots - 11\!\cdots\!00 \)
T^3 + 29956565300*T^2 - 15907835544642102715600*T - 117192287228342687755848960680000
$23$
\( T^{3} - 16254077844 T^{2} + \cdots - 46\!\cdots\!96 \)
T^3 - 16254077844*T^2 - 349948557045023628335616*T - 4646349143028605414807274869565696
$29$
\( T^{3} + 2528278831750 T^{2} + \cdots - 11\!\cdots\!00 \)
T^3 + 2528278831750*T^2 - 7814293790829483813274100*T - 11972285729039037228666852855376875000
$31$
\( T^{3} + 521256054664 T^{2} + \cdots - 29\!\cdots\!28 \)
T^3 + 521256054664*T^2 - 35451802378223004894202368*T - 29585862511060183183995988833176444928
$37$
\( T^{3} - 31762746900498 T^{2} + \cdots - 72\!\cdots\!48 \)
T^3 - 31762746900498*T^2 + 287946948751517624737748076*T - 720636836633900178177436139764682258648
$41$
\( T^{3} - 86833482954446 T^{2} + \cdots + 65\!\cdots\!32 \)
T^3 - 86833482954446*T^2 + 1339001008201377270441268972*T + 6537805024307363475267995645416409087832
$43$
\( T^{3} - 89258046385744 T^{2} + \cdots + 13\!\cdots\!84 \)
T^3 - 89258046385744*T^2 - 5381747772477825038501682736*T + 136750017785308314923816680819183697555584
$47$
\( T^{3} - 348182738140228 T^{2} + \cdots + 11\!\cdots\!32 \)
T^3 - 348182738140228*T^2 - 23627135267468733197258735744*T + 11726141314116387848433624199309197033618432
$53$
\( T^{3} - 44014499212594 T^{2} + \cdots + 57\!\cdots\!24 \)
T^3 - 44014499212594*T^2 - 304838366976289485277709650196*T + 57760323955812225086524067905291987828986024
$59$
\( T^{3} + \cdots + 10\!\cdots\!00 \)
T^3 + 2133293278957100*T^2 + 916060447168279812943253815600*T + 101992162999959867135342082889245814083560000
$61$
\( T^{3} + \cdots + 35\!\cdots\!52 \)
T^3 - 2822990449991866*T^2 - 877204996056369999712711279348*T + 3573224645447366026548421366346133560828198152
$67$
\( T^{3} - 374173462156688 T^{2} + \cdots - 20\!\cdots\!08 \)
T^3 - 374173462156688*T^2 - 15229013587702796564753002820784*T - 20985200447536931265657508659500246984959943808
$71$
\( T^{3} + \cdots + 16\!\cdots\!12 \)
T^3 + 9029705707562224*T^2 + 24174223405442385394189602275392*T + 16244004112949758561495737854702670182158221312
$73$
\( T^{3} + \cdots - 48\!\cdots\!96 \)
T^3 + 5906564941861106*T^2 - 5858120007110476733611158096916*T - 48838677522922839670186803285572469823491254696
$79$
\( T^{3} + \cdots + 13\!\cdots\!00 \)
T^3 - 9183397142621600*T^2 - 131286273905830828322566289913600*T + 132917814506455181904852837423837303354408960000
$83$
\( T^{3} + \cdots - 16\!\cdots\!56 \)
T^3 - 15992201117651544*T^2 - 843720500559405397227250308232176*T - 1631669152314900861031417843981357194037323814656
$89$
\( T^{3} + \cdots - 17\!\cdots\!00 \)
T^3 + 31272661736951250*T^2 - 606461548177721283090070159242900*T - 17687522278932018405853064192464257888516362025000
$97$
\( T^{3} + \cdots + 54\!\cdots\!32 \)
T^3 - 28207632381796278*T^2 - 1795700288332687647766514467649844*T + 54219451652091379276268024697171497861854448005432
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