[N,k,chi] = [520,6,Mod(1,520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("520.1");
S:= CuspForms(chi, 6);
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
p p p
Sign
2 2 2
+ 1 +1 + 1
5 5 5
+ 1 +1 + 1
13 13 1 3
− 1 -1 − 1
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
T 3 8 + 16 T 3 7 − 1280 T 3 6 − 17216 T 3 5 + 449704 T 3 4 + 5029696 T 3 3 + ⋯ − 580250736 T_{3}^{8} + 16 T_{3}^{7} - 1280 T_{3}^{6} - 17216 T_{3}^{5} + 449704 T_{3}^{4} + 5029696 T_{3}^{3} + \cdots - 580250736 T 3 8 + 1 6 T 3 7 − 1 2 8 0 T 3 6 − 1 7 2 1 6 T 3 5 + 4 4 9 7 0 4 T 3 4 + 5 0 2 9 6 9 6 T 3 3 + ⋯ − 5 8 0 2 5 0 7 3 6
T3^8 + 16*T3^7 - 1280*T3^6 - 17216*T3^5 + 449704*T3^4 + 5029696*T3^3 - 31668480*T3^2 - 372522240*T3 - 580250736
acting on S 6 n e w ( Γ 0 ( 520 ) ) S_{6}^{\mathrm{new}}(\Gamma_0(520)) S 6 n e w ( Γ 0 ( 5 2 0 ) ) .
p p p
F p ( T ) F_p(T) F p ( T )
2 2 2
T 8 T^{8} T 8
T^8
3 3 3
T 8 + 16 T 7 + ⋯ − 580250736 T^{8} + 16 T^{7} + \cdots - 580250736 T 8 + 1 6 T 7 + ⋯ − 5 8 0 2 5 0 7 3 6
T^8 + 16*T^7 - 1280*T^6 - 17216*T^5 + 449704*T^4 + 5029696*T^3 - 31668480*T^2 - 372522240*T - 580250736
5 5 5
( T + 25 ) 8 (T + 25)^{8} ( T + 2 5 ) 8
(T + 25)^8
7 7 7
T 8 + ⋯ − 99 ⋯ 80 T^{8} + \cdots - 99\!\cdots\!80 T 8 + ⋯ − 9 9 ⋯ 8 0
T^8 - 184*T^7 - 49616*T^6 + 11921952*T^5 + 114540576*T^4 - 153104429184*T^3 + 6743920898304*T^2 + 233204843146752*T - 9936699883303680
11 11 1 1
T 8 + ⋯ − 22 ⋯ 08 T^{8} + \cdots - 22\!\cdots\!08 T 8 + ⋯ − 2 2 ⋯ 0 8
T^8 - 128*T^7 - 881816*T^6 - 2426576*T^5 + 221239002232*T^4 + 24036304659712*T^3 - 11697784970447840*T^2 - 1658077180223676992*T - 22112793134870658608
13 13 1 3
( T − 169 ) 8 (T - 169)^{8} ( T − 1 6 9 ) 8
(T - 169)^8
17 17 1 7
T 8 + ⋯ + 22 ⋯ 40 T^{8} + \cdots + 22\!\cdots\!40 T 8 + ⋯ + 2 2 ⋯ 4 0
T^8 - 1656*T^7 - 4742880*T^6 + 5996279392*T^5 + 8334836227872*T^4 - 5023390128610944*T^3 - 5849930300277386240*T^2 - 560904505260640206336*T + 222781387115145309431040
19 19 1 9
T 8 + ⋯ + 11 ⋯ 36 T^{8} + \cdots + 11\!\cdots\!36 T 8 + ⋯ + 1 1 ⋯ 3 6
T^8 + 2112*T^7 - 12280872*T^6 - 19071050128*T^5 + 50255272467864*T^4 + 48676584002071296*T^3 - 57282808181492649248*T^2 - 48135316050665340254016*T + 1134477819416564737017936
23 23 2 3
T 8 + ⋯ + 41 ⋯ 12 T^{8} + \cdots + 41\!\cdots\!12 T 8 + ⋯ + 4 1 ⋯ 1 2
T^8 + 1144*T^7 - 24966416*T^6 - 15180758864*T^5 + 151329631417768*T^4 - 5578350496192928*T^3 - 207124008776425080128*T^2 + 13161995147331244588480*T + 41332535556289101378957712
29 29 2 9
T 8 + ⋯ + 23 ⋯ 36 T^{8} + \cdots + 23\!\cdots\!36 T 8 + ⋯ + 2 3 ⋯ 3 6
T^8 + 6672*T^7 - 47336736*T^6 - 489008825088*T^5 - 1155138033269376*T^4 - 247201729289542656*T^3 + 1313999295398746970112*T^2 + 1079061563221098834345984*T + 237601175305970818073972736
31 31 3 1
T 8 + ⋯ + 35 ⋯ 40 T^{8} + \cdots + 35\!\cdots\!40 T 8 + ⋯ + 3 5 ⋯ 4 0
T^8 + 2984*T^7 - 96497816*T^6 - 45344791168*T^5 + 2446415750028376*T^4 - 1186538363595661024*T^3 - 17534215577102799094496*T^2 + 5823661988374813186700288*T + 35171817344215098502965244240
37 37 3 7
T 8 + ⋯ + 58 ⋯ 00 T^{8} + \cdots + 58\!\cdots\!00 T 8 + ⋯ + 5 8 ⋯ 0 0
T^8 + 13432*T^7 - 138325280*T^6 - 1558083492864*T^5 + 3907664376581376*T^4 + 43399246313527916544*T^3 + 21674988247160588230656*T^2 - 125439937229782284652707840*T + 58572016336542226228582809600
41 41 4 1
T 8 + ⋯ − 49 ⋯ 64 T^{8} + \cdots - 49\!\cdots\!64 T 8 + ⋯ − 4 9 ⋯ 6 4
T^8 + 10136*T^7 - 234620384*T^6 - 1949552399840*T^5 + 15552111268140320*T^4 + 84503263429971356800*T^3 - 250541148750947152047104*T^2 - 833436089129916876745214464*T - 496225136742796210639786244864
43 43 4 3
T 8 + ⋯ + 73 ⋯ 88 T^{8} + \cdots + 73\!\cdots\!88 T 8 + ⋯ + 7 3 ⋯ 8 8
T^8 + 3632*T^7 - 488035664*T^6 - 5226813387744*T^5 + 29725530380804424*T^4 + 710944358575459680960*T^3 + 4002420117664465013797056*T^2 + 9209639011841713039085799552*T + 7334464831240300088797097679888
47 47 4 7
T 8 + ⋯ + 51 ⋯ 28 T^{8} + \cdots + 51\!\cdots\!28 T 8 + ⋯ + 5 1 ⋯ 2 8
T^8 - 25256*T^7 - 1071955856*T^6 + 24964668509024*T^5 + 415932575641126688*T^4 - 7809284608011147587968*T^3 - 73408493902009596539077376*T^2 + 780473173638463674654190328320*T + 5112092418195932541082064843676928
53 53 5 3
T 8 + ⋯ + 12 ⋯ 32 T^{8} + \cdots + 12\!\cdots\!32 T 8 + ⋯ + 1 2 ⋯ 3 2
T^8 - 26744*T^7 - 1009188704*T^6 + 23127782780768*T^5 + 344394322508507936*T^4 - 4652718199819951470208*T^3 - 50416360192963706499691520*T^2 + 2881725376356657935408894464*T + 125643908535287946725480252876032
59 59 5 9
T 8 + ⋯ + 64 ⋯ 12 T^{8} + \cdots + 64\!\cdots\!12 T 8 + ⋯ + 6 4 ⋯ 1 2
T^8 - 55344*T^7 - 2990852328*T^6 + 232641833027952*T^5 - 751417813759506984*T^4 - 221562208232051145554880*T^3 + 5355141301788421660990168032*T^2 - 40380622154520786761811921850176*T + 64212938148359162478197511436287312
61 61 6 1
T 8 + ⋯ − 22 ⋯ 00 T^{8} + \cdots - 22\!\cdots\!00 T 8 + ⋯ − 2 2 ⋯ 0 0
T^8 - 22784*T^7 - 4464044384*T^6 + 106559550388096*T^5 + 6158621966937180544*T^4 - 155215433060079165550592*T^3 - 2423229231258446822171850752*T^2 + 69682152151385258830914225233920*T - 228110780336342004102126273654272000
67 67 6 7
T 8 + ⋯ − 89 ⋯ 04 T^{8} + \cdots - 89\!\cdots\!04 T 8 + ⋯ − 8 9 ⋯ 0 4
T^8 - 16984*T^7 - 2927216864*T^6 + 28213170253152*T^5 + 2458763468836836576*T^4 - 6161499419728486079616*T^3 - 596872302995658473369750016*T^2 - 4358313297610930598136982801920*T - 8975303543731897444723318272962304
71 71 7 1
T 8 + ⋯ − 21 ⋯ 52 T^{8} + \cdots - 21\!\cdots\!52 T 8 + ⋯ − 2 1 ⋯ 5 2
T^8 - 118856*T^7 + 454215784*T^6 + 444299287237952*T^5 - 21496963990467690088*T^4 + 410421057381735304101728*T^3 - 3618946160103781560097895648*T^2 + 14618170460948783434378691687680*T - 21770728619535978313598588391787952
73 73 7 3
T 8 + ⋯ − 39 ⋯ 76 T^{8} + \cdots - 39\!\cdots\!76 T 8 + ⋯ − 3 9 ⋯ 7 6
T^8 - 120744*T^7 - 3847086048*T^6 + 732989888052736*T^5 + 367287811477317888*T^4 - 1219596454953068167317504*T^3 + 5707463097987295591939465216*T^2 + 431494062678887698570935731552256*T - 3960402112241583582837170717426712576
79 79 7 9
T 8 + ⋯ − 95 ⋯ 32 T^{8} + \cdots - 95\!\cdots\!32 T 8 + ⋯ − 9 5 ⋯ 3 2
T^8 - 154720*T^7 - 1303497152*T^6 + 1005162489630464*T^5 - 30628179456017072000*T^4 - 569785442024880947697664*T^3 + 24027150563265945697849348096*T^2 - 43624787665416110259705910018048*T - 955885559043217368419318440327442432
83 83 8 3
T 8 + ⋯ + 47 ⋯ 92 T^{8} + \cdots + 47\!\cdots\!92 T 8 + ⋯ + 4 7 ⋯ 9 2
T^8 - 179048*T^7 - 1527252272*T^6 + 1985866589363424*T^5 - 111527970764172206688*T^4 - 1008661870053073620710784*T^3 + 232930285377676091597809886976*T^2 - 6073230447102867356593679015443968*T + 47717381656519734480550571322429633792
89 89 8 9
T 8 + ⋯ + 88 ⋯ 00 T^{8} + \cdots + 88\!\cdots\!00 T 8 + ⋯ + 8 8 ⋯ 0 0
T^8 - 254336*T^7 + 13523217808*T^6 + 1023010210026624*T^5 - 77707510430042222880*T^4 - 1904631638621965594801152*T^3 + 106676719978115633349458730240*T^2 + 2829088590492600663238513795737600*T + 8832644137686728714399792916094368000
97 97 9 7
T 8 + ⋯ − 18 ⋯ 00 T^{8} + \cdots - 18\!\cdots\!00 T 8 + ⋯ − 1 8 ⋯ 0 0
T^8 - 134320*T^7 - 38823454544*T^6 + 5610182807371712*T^5 + 235100485824116942176*T^4 - 58357361961280253977089280*T^3 + 1871148515739751107642530050816*T^2 + 39245834211158369169217026663007232*T - 1895460851196757035749895539528366739200
show more
show less