[N,k,chi] = [64,22,Mod(1,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.1");
S:= CuspForms(chi, 22);
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
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{3} + 96764T_{3}^{2} - 20431242576T_{3} + 156439878638400 \)
T3^3 + 96764*T3^2 - 20431242576*T3 + 156439878638400
acting on \(S_{22}^{\mathrm{new}}(\Gamma_0(64))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( T^{3} + \cdots + 156439878638400 \)
T^3 + 96764*T^2 - 20431242576*T + 156439878638400
$5$
\( T^{3} - 24111774 T^{2} + \cdots + 22\!\cdots\!00 \)
T^3 - 24111774*T^2 - 988349133810900*T + 22232142716343413695000
$7$
\( T^{3} - 295988280 T^{2} + \cdots + 35\!\cdots\!56 \)
T^3 - 295988280*T^2 - 368812599188427072*T + 35553267238349450938553856
$11$
\( T^{3} - 40335108684 T^{2} + \cdots + 59\!\cdots\!44 \)
T^3 - 40335108684*T^2 - 10441954462928913022416*T + 59524752563419325669726498167744
$13$
\( T^{3} + 133734425946 T^{2} + \cdots + 64\!\cdots\!48 \)
T^3 + 133734425946*T^2 - 115098792875405225576820*T + 6472174164833194012324148941520248
$17$
\( T^{3} - 7797732274422 T^{2} + \cdots + 13\!\cdots\!00 \)
T^3 - 7797732274422*T^2 - 175713729547804795693822260*T + 1324949703836841726808989570114822854200
$19$
\( T^{3} + 35788199781996 T^{2} + \cdots + 14\!\cdots\!64 \)
T^3 + 35788199781996*T^2 + 304370510333927276928827184*T + 1425738420978845579396279176799065664
$23$
\( T^{3} - 193770761479080 T^{2} + \cdots + 13\!\cdots\!24 \)
T^3 - 193770761479080*T^2 - 86213799465445083704509369152*T + 13187283552587307446366891509614797597479424
$29$
\( T^{3} + \cdots + 45\!\cdots\!12 \)
T^3 + 5607343422466122*T^2 + 9071478183922886643161316725196*T + 4539413024449715535736469217571334882219174712
$31$
\( T^{3} + \cdots - 23\!\cdots\!00 \)
T^3 - 11246757871503072*T^2 + 34730306601643932286077451791360*T - 23815531358787205788296262423516721428441497600
$37$
\( T^{3} + \cdots + 15\!\cdots\!16 \)
T^3 - 24272499791100606*T^2 - 830562241962896743358222496702036*T + 15491175144651199711548946573428922329512373624216
$41$
\( T^{3} + \cdots + 68\!\cdots\!24 \)
T^3 + 298159108991869602*T^2 + 25705697452807969271020275554023980*T + 682682244791993949461002798777716495182684271456024
$43$
\( T^{3} + \cdots - 88\!\cdots\!08 \)
T^3 - 33333932139754860*T^2 - 29470189182790362000487752607385808*T - 887175698016699726736323863486739096590140393260608
$47$
\( T^{3} + \cdots - 79\!\cdots\!64 \)
T^3 + 120874283547603888*T^2 - 398972777779486261277132360967965952*T - 79030407514911718236255332842532460026835279168958464
$53$
\( T^{3} + \cdots + 28\!\cdots\!76 \)
T^3 - 1138443393004854222*T^2 - 125978547888349244673772890448241172*T + 284423045491652872720017065853366511462763865514745176
$59$
\( T^{3} + \cdots - 10\!\cdots\!56 \)
T^3 + 9225624498709937412*T^2 - 1317596243250574505275979197278526800*T - 109852800450935440695562440827015787836603720112856705856
$61$
\( T^{3} + \cdots + 14\!\cdots\!00 \)
T^3 - 6554902294063924182*T^2 - 20127818242176427305938006561503407540*T + 142616542823560215737805842663275350499304657022004886200
$67$
\( T^{3} + \cdots + 42\!\cdots\!48 \)
T^3 - 15793054074531629124*T^2 - 60879887424609609214563462223790821200*T + 427642881117395197918929380929951975527066981752809379648
$71$
\( T^{3} + \cdots - 34\!\cdots\!00 \)
T^3 + 41139582493467997704*T^2 - 909655798496155836384343412609489253696*T - 34075829930628978583795667062317168738876519270969338124800
$73$
\( T^{3} + \cdots - 28\!\cdots\!56 \)
T^3 + 19422167949903851970*T^2 - 249864080979506983216201233138279364692*T - 2849523567747148932946034203357249953114615850835374948456
$79$
\( T^{3} + \cdots - 47\!\cdots\!00 \)
T^3 + 131735321299806049488*T^2 - 2435514001940510088143039378560898014464*T - 476496014476853269504318106035757821809474314313337231052800
$83$
\( T^{3} + \cdots + 44\!\cdots\!76 \)
T^3 + 64013993832679681068*T^2 - 29225919704070059779421947421151234601680*T + 449639703892492830399135106687059395442514068388941577318976
$89$
\( T^{3} + \cdots + 24\!\cdots\!76 \)
T^3 - 429891446897537246766*T^2 - 47460975537980818038183538970702222924436*T + 24024093868397735630376515464697869841866586435027748444553176
$97$
\( T^{3} + \cdots + 10\!\cdots\!44 \)
T^3 + 324059336514148638042*T^2 - 538933405515470239165130834825978888202612*T + 102498063074430008141891262750313561678664841774661971873389944
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