[N,k,chi] = [128,12,Mod(1,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.1");
S:= CuspForms(chi, 12);
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 ι m \iota_m ι m of the coefficient field, the values ι m ( a n ) \iota_m(a_n) ι 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 intersection of the kernels of the following linear operators acting on S 12 n e w ( Γ 0 ( 128 ) ) S_{12}^{\mathrm{new}}(\Gamma_0(128)) S 1 2 n e w ( Γ 0 ( 1 2 8 ) ) :
T 3 6 + 20 T 3 5 − 688148 T 3 4 + 32764128 T 3 3 + 81557676144 T 3 2 + 8149590626112 T 3 − 297910794836160 T_{3}^{6} + 20T_{3}^{5} - 688148T_{3}^{4} + 32764128T_{3}^{3} + 81557676144T_{3}^{2} + 8149590626112T_{3} - 297910794836160 T 3 6 + 2 0 T 3 5 − 6 8 8 1 4 8 T 3 4 + 3 2 7 6 4 1 2 8 T 3 3 + 8 1 5 5 7 6 7 6 1 4 4 T 3 2 + 8 1 4 9 5 9 0 6 2 6 1 1 2 T 3 − 2 9 7 9 1 0 7 9 4 8 3 6 1 6 0
T3^6 + 20*T3^5 - 688148*T3^4 + 32764128*T3^3 + 81557676144*T3^2 + 8149590626112*T3 - 297910794836160
T 5 6 + 1804 T 5 5 − 170673668 T 5 4 + 115715684000 T 5 3 + ⋯ − 39 ⋯ 00 T_{5}^{6} + 1804 T_{5}^{5} - 170673668 T_{5}^{4} + 115715684000 T_{5}^{3} + \cdots - 39\!\cdots\!00 T 5 6 + 1 8 0 4 T 5 5 − 1 7 0 6 7 3 6 6 8 T 5 4 + 1 1 5 7 1 5 6 8 4 0 0 0 T 5 3 + ⋯ − 3 9 ⋯ 0 0
T5^6 + 1804*T5^5 - 170673668*T5^4 + 115715684000*T5^3 + 4859111696284400*T5^2 - 2525582262156040000*T5 - 39240696416089937880000
p p p
F p ( T ) F_p(T) F p ( T )
2 2 2
T 6 T^{6} T 6
T^6
3 3 3
T 6 + ⋯ − 297910794836160 T^{6} + \cdots - 297910794836160 T 6 + ⋯ − 2 9 7 9 1 0 7 9 4 8 3 6 1 6 0
T^6 + 20*T^5 - 688148*T^4 + 32764128*T^3 + 81557676144*T^2 + 8149590626112*T - 297910794836160
5 5 5
T 6 + ⋯ − 39 ⋯ 00 T^{6} + \cdots - 39\!\cdots\!00 T 6 + ⋯ − 3 9 ⋯ 0 0
T^6 + 1804*T^5 - 170673668*T^4 + 115715684000*T^3 + 4859111696284400*T^2 - 2525582262156040000*T - 39240696416089937880000
7 7 7
T 6 + ⋯ + 24 ⋯ 40 T^{6} + \cdots + 24\!\cdots\!40 T 6 + ⋯ + 2 4 ⋯ 4 0
T^6 - 49368*T^5 - 5636820048*T^4 + 242979558680320*T^3 + 4899045674863200000*T^2 - 273258668787447682504704*T + 2403115200023723551044259840
11 11 1 1
T 6 + ⋯ − 55 ⋯ 28 T^{6} + \cdots - 55\!\cdots\!28 T 6 + ⋯ − 5 5 ⋯ 2 8
T^6 + 688460*T^5 - 1182468870484*T^4 - 661015093066847712*T^3 + 439360774982373879737968*T^2 + 144342177328999212793648803520*T - 55107586746134273801495884942376128
13 13 1 3
T 6 + ⋯ − 31 ⋯ 40 T^{6} + \cdots - 31\!\cdots\!40 T 6 + ⋯ − 3 1 ⋯ 4 0
T^6 + 2290348*T^5 - 4133038867652*T^4 - 13933144788566622304*T^3 - 9210412660931017704475408*T^2 - 492411642187854328840524109120*T - 3110833355069697583211576446050240
17 17 1 7
T 6 + ⋯ − 49 ⋯ 40 T^{6} + \cdots - 49\!\cdots\!40 T 6 + ⋯ − 4 9 ⋯ 4 0
T^6 - 4127636*T^5 - 67566655192580*T^4 + 485549758952060247968*T^3 - 1189156640440493721924571408*T^2 + 1262654889172696468559613820149440*T - 495068710686031757313824996275080008640
19 19 1 9
T 6 + ⋯ + 21 ⋯ 40 T^{6} + \cdots + 21\!\cdots\!40 T 6 + ⋯ + 2 1 ⋯ 4 0
T^6 - 9936364*T^5 - 443148910286612*T^4 + 5662093069893663414496*T^3 + 33618923782699570338794936432*T^2 - 677805889121898754061244056754925760*T + 2180215972470019125272460931784224165803840
23 23 2 3
T 6 + ⋯ − 21 ⋯ 96 T^{6} + \cdots - 21\!\cdots\!96 T 6 + ⋯ − 2 1 ⋯ 9 6
T^6 - 9921320*T^5 - 2117299308720208*T^4 + 19767936213799839979776*T^3 + 1294703007768227702102419244800*T^2 - 8513116203342306845724615076534872064*T - 218473003204497434054829544233596447324778496
29 29 2 9
T 6 + ⋯ − 11 ⋯ 28 T^{6} + \cdots - 11\!\cdots\!28 T 6 + ⋯ − 1 1 ⋯ 2 8
T^6 - 25222532*T^5 - 41097462016036836*T^4 + 817892161380764401974816*T^3 + 278240262290243237838851560830960*T^2 - 9755865179766896690050939556042666789952*T - 11157320973879571461708712123143204340367636928
31 31 3 1
T 6 + ⋯ + 20 ⋯ 48 T^{6} + \cdots + 20\!\cdots\!48 T 6 + ⋯ + 2 0 ⋯ 4 8
T^6 + 246133120*T^5 - 86179490460082176*T^4 - 23370050686615592210792448*T^3 + 952731092720133924333605319868416*T^2 + 458659484136285612440788985607114857644032*T + 20973276918871656051016376141895232994075002011648
37 37 3 7
T 6 + ⋯ + 15 ⋯ 12 T^{6} + \cdots + 15\!\cdots\!12 T 6 + ⋯ + 1 5 ⋯ 1 2
T^6 + 660146172*T^5 - 716190037119619812*T^4 - 533583134964503895890032096*T^3 + 66698401295973744055336195047866352*T^2 + 98443796680500727139519732720352444977228736*T + 15681578501721541884484673010992552582674458304501312
41 41 4 1
T 6 + ⋯ + 75 ⋯ 92 T^{6} + \cdots + 75\!\cdots\!92 T 6 + ⋯ + 7 5 ⋯ 9 2
T^6 - 486915836*T^5 - 1548247943125762212*T^4 + 49527332147225050980144096*T^3 + 532622405264944112408971518054807024*T^2 + 139875600272853758874380237159874254616132672*T + 7542944128883772522334883789752272638266656908016192
43 43 4 3
T 6 + ⋯ − 91 ⋯ 00 T^{6} + \cdots - 91\!\cdots\!00 T 6 + ⋯ − 9 1 ⋯ 0 0
T^6 - 1147261348*T^5 - 2290600936205993076*T^4 + 2140552953154544623400573088*T^3 + 1264290214689223275227046514003791216*T^2 - 794037691467663858753214865628516741282507840*T - 91898982072669611608555110084117460138424976060753600
47 47 4 7
T 6 + ⋯ + 16 ⋯ 00 T^{6} + \cdots + 16\!\cdots\!00 T 6 + ⋯ + 1 6 ⋯ 0 0
T^6 - 603975088*T^5 - 6124988062369892672*T^4 - 3259181067617402515443402752*T^3 + 5923536759446935442506948422128660480*T^2 + 6288027784589558232167040732015874823283343360*T + 1615210336832103993810041174027461466072949472867123200
53 53 5 3
T 6 + ⋯ − 19 ⋯ 40 T^{6} + \cdots - 19\!\cdots\!40 T 6 + ⋯ − 1 9 ⋯ 4 0
T^6 + 428043996*T^5 - 25173448013553948708*T^4 - 5625209914638441907838726880*T^3 + 143000357627341434917266379136899413488*T^2 - 6202438570938156573929431170036112680321248832*T - 196908902032953852142930952677620192596103159988356181440
59 59 5 9
T 6 + ⋯ − 14 ⋯ 80 T^{6} + \cdots - 14\!\cdots\!80 T 6 + ⋯ − 1 4 ⋯ 8 0
T^6 - 809510676*T^5 - 90937922267307982356*T^4 + 6084848845607258357393643296*T^3 + 1706612305742432752888384200300259487856*T^2 + 2492090029247212205470420193766001356438905094336*T - 149490445766021358514698132907018025512310283160047270080
61 61 6 1
T 6 + ⋯ + 71 ⋯ 20 T^{6} + \cdots + 71\!\cdots\!20 T 6 + ⋯ + 7 1 ⋯ 2 0
T^6 + 2822052332*T^5 - 51448836810576180292*T^4 - 236880858326388559717578849888*T^3 + 38413604217336261963782968823911856368*T^2 + 1127343666945558164689137396590463300679295643328*T + 717757172688976439382351416318000551539441572350769760320
67 67 6 7
T 6 + ⋯ − 22 ⋯ 76 T^{6} + \cdots - 22\!\cdots\!76 T 6 + ⋯ − 2 2 ⋯ 7 6
T^6 - 9742675036*T^5 - 158875571179835171188*T^4 + 1286011109007345466127652020064*T^3 + 3734121848586706416433689407449518863728*T^2 - 25749118531493421429689920741996581978825839907776*T - 22388379725389500948966474934109067023446377121112817923776
71 71 7 1
T 6 + ⋯ + 10 ⋯ 20 T^{6} + \cdots + 10\!\cdots\!20 T 6 + ⋯ + 1 0 ⋯ 2 0
T^6 - 16181067512*T^5 - 100486306081841853648*T^4 + 2021449756753313844191736410880*T^3 - 2579988447310846599263876975468910086400*T^2 - 39114601372914164973293211694082224467894560864256*T + 100407387864321325737968934648117793091430072222174715269120
73 73 7 3
T 6 + ⋯ − 29 ⋯ 80 T^{6} + \cdots - 29\!\cdots\!80 T 6 + ⋯ − 2 9 ⋯ 8 0
T^6 - 35963668692*T^5 - 539406170069315209860*T^4 + 35792240644626253974837466893728*T^3 - 494860257705448382879023613717169802016016*T^2 + 2463778009970060960223890596838839253593283752032960*T - 2939042217648816368421026810506914557286453772519718633094080
79 79 7 9
T 6 + ⋯ + 13 ⋯ 60 T^{6} + \cdots + 13\!\cdots\!60 T 6 + ⋯ + 1 3 ⋯ 6 0
T^6 + 6103946192*T^5 - 2766754973232892185920*T^4 - 27576924581808670797741570394112*T^3 + 1729552922526067847609039089788440403931136*T^2 + 30764161833527668909801136929021077953318627063431168*T + 132969851266952989832453423448715903573012780492778579994869760
83 83 8 3
T 6 + ⋯ − 31 ⋯ 72 T^{6} + \cdots - 31\!\cdots\!72 T 6 + ⋯ − 3 1 ⋯ 7 2
T^6 - 67929536124*T^5 - 52270834938675858996*T^4 + 29610472407444925674971557394016*T^3 + 286673826445332860689596080189549277382512*T^2 + 600811888602332197464787790575890370230768533287488*T - 318064428499988567553469425989352828611907038934364734190272
89 89 8 9
T 6 + ⋯ − 60 ⋯ 84 T^{6} + \cdots - 60\!\cdots\!84 T 6 + ⋯ − 6 0 ⋯ 8 4
T^6 - 22721416116*T^5 - 8987670934125847827012*T^4 - 11609680773157579226430006246752*T^3 + 19771692736789719367071146785829331413867760*T^2 + 235682518540455941935894876982210334514966878526289088*T - 6045874232564525454925464819632177357494237940392307886642382784
97 97 9 7
T 6 + ⋯ − 23 ⋯ 84 T^{6} + \cdots - 23\!\cdots\!84 T 6 + ⋯ − 2 3 ⋯ 8 4
T^6 - 218896625492*T^5 - 1303726551573803080580*T^4 + 3295494533725926920428605577071008*T^3 - 245693562531830982746641709832122668743326992*T^2 + 5043131591945523769421749422486362375974277861309215424*T - 23647952007454902255275283361690741145713869598959624366343195584
show more
show less