[N,k,chi] = [483,4,Mod(1,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("483.1");
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 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
3 3 3
− 1 -1 − 1
7 7 7
− 1 -1 − 1
23 23 2 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 2 9 − 8 T 2 8 − 23 T 2 7 + 267 T 2 6 + 64 T 2 5 − 2685 T 2 4 + 526 T 2 3 + 8786 T 2 2 − 1400 T 2 − 5336 T_{2}^{9} - 8T_{2}^{8} - 23T_{2}^{7} + 267T_{2}^{6} + 64T_{2}^{5} - 2685T_{2}^{4} + 526T_{2}^{3} + 8786T_{2}^{2} - 1400T_{2} - 5336 T 2 9 − 8 T 2 8 − 2 3 T 2 7 + 2 6 7 T 2 6 + 6 4 T 2 5 − 2 6 8 5 T 2 4 + 5 2 6 T 2 3 + 8 7 8 6 T 2 2 − 1 4 0 0 T 2 − 5 3 3 6
T2^9 - 8*T2^8 - 23*T2^7 + 267*T2^6 + 64*T2^5 - 2685*T2^4 + 526*T2^3 + 8786*T2^2 - 1400*T2 - 5336
acting on S 4 n e w ( Γ 0 ( 483 ) ) S_{4}^{\mathrm{new}}(\Gamma_0(483)) S 4 n e w ( Γ 0 ( 4 8 3 ) ) .
p p p
F p ( T ) F_p(T) F p ( T )
2 2 2
T 9 − 8 T 8 + ⋯ − 5336 T^{9} - 8 T^{8} + \cdots - 5336 T 9 − 8 T 8 + ⋯ − 5 3 3 6
T^9 - 8*T^8 - 23*T^7 + 267*T^6 + 64*T^5 - 2685*T^4 + 526*T^3 + 8786*T^2 - 1400*T - 5336
3 3 3
( T − 3 ) 9 (T - 3)^{9} ( T − 3 ) 9
(T - 3)^9
5 5 5
T 9 − 39 T 8 + ⋯ + 919405312 T^{9} - 39 T^{8} + \cdots + 919405312 T 9 − 3 9 T 8 + ⋯ + 9 1 9 4 0 5 3 1 2
T^9 - 39*T^8 + 21*T^7 + 14541*T^6 - 127509*T^5 - 1125093*T^4 + 15602526*T^3 - 4331496*T^2 - 396647936*T + 919405312
7 7 7
( T − 7 ) 9 (T - 7)^{9} ( T − 7 ) 9
(T - 7)^9
11 11 1 1
T 9 + ⋯ − 4877431083904 T^{9} + \cdots - 4877431083904 T 9 + ⋯ − 4 8 7 7 4 3 1 0 8 3 9 0 4
T^9 - 38*T^8 - 4955*T^7 + 241002*T^6 + 3869923*T^5 - 302081450*T^4 + 992506911*T^3 + 100159289286*T^2 - 785287342472*T - 4877431083904
13 13 1 3
T 9 + ⋯ − 11393014127088 T^{9} + \cdots - 11393014127088 T 9 + ⋯ − 1 1 3 9 3 0 1 4 1 2 7 0 8 8
T^9 - 107*T^8 - 2805*T^7 + 598645*T^6 - 7938275*T^5 - 824861037*T^4 + 18325016804*T^3 + 328442381216*T^2 - 8001688712992*T - 11393014127088
17 17 1 7
T 9 + ⋯ − 11 ⋯ 56 T^{9} + \cdots - 11\!\cdots\!56 T 9 + ⋯ − 1 1 ⋯ 5 6
T^9 - 170*T^8 - 5048*T^7 + 1874282*T^6 - 24033965*T^5 - 6191863624*T^4 + 142323584060*T^3 + 5531332150896*T^2 - 110395709796352*T - 1125493742496256
19 19 1 9
T 9 + ⋯ − 31 ⋯ 12 T^{9} + \cdots - 31\!\cdots\!12 T 9 + ⋯ − 3 1 ⋯ 1 2
T^9 - 20*T^8 - 40017*T^7 + 1358390*T^6 + 474804887*T^5 - 23791358176*T^4 - 1431787656415*T^3 + 93881436487646*T^2 - 738536954908360*T - 3114681419280512
23 23 2 3
( T + 23 ) 9 (T + 23)^{9} ( T + 2 3 ) 9
(T + 23)^9
29 29 2 9
T 9 + ⋯ + 59 ⋯ 04 T^{9} + \cdots + 59\!\cdots\!04 T 9 + ⋯ + 5 9 ⋯ 0 4
T^9 - 405*T^8 + 4894*T^7 + 13353214*T^6 - 897813259*T^5 - 103876512009*T^4 + 6238537578572*T^3 + 242697802208176*T^2 - 8767450139897600*T + 59977162949601104
31 31 3 1
T 9 + ⋯ + 11 ⋯ 12 T^{9} + \cdots + 11\!\cdots\!12 T 9 + ⋯ + 1 1 ⋯ 1 2
T^9 + 182*T^8 - 117462*T^7 - 18116212*T^6 + 4048509609*T^5 + 516196285430*T^4 - 48023928028004*T^3 - 5065683031830488*T^2 + 122136649450105344*T + 11300260220057984512
37 37 3 7
T 9 + ⋯ − 32 ⋯ 68 T^{9} + \cdots - 32\!\cdots\!68 T 9 + ⋯ − 3 2 ⋯ 6 8
T^9 - 347*T^8 - 188552*T^7 + 65643690*T^6 + 10009563109*T^5 - 3617219022499*T^4 - 149809492458454*T^3 + 62836885908243044*T^2 + 707552015912216904*T - 329434852328681731168
41 41 4 1
T 9 + ⋯ + 17 ⋯ 24 T^{9} + \cdots + 17\!\cdots\!24 T 9 + ⋯ + 1 7 ⋯ 2 4
T^9 - 717*T^8 - 12911*T^7 + 79941899*T^6 - 8465531025*T^5 - 391872858419*T^4 + 63608053889211*T^3 - 954467532065271*T^2 - 68535404968785724*T + 1741486924909622124
43 43 4 3
T 9 + ⋯ + 21 ⋯ 36 T^{9} + \cdots + 21\!\cdots\!36 T 9 + ⋯ + 2 1 ⋯ 3 6
T^9 + 77*T^8 - 369851*T^7 - 45289709*T^6 + 38256986405*T^5 + 6278651855813*T^4 - 1179033086540734*T^3 - 226640838705512792*T^2 + 9271865637277308512*T + 2163463353796093854336
47 47 4 7
T 9 + ⋯ + 51 ⋯ 08 T^{9} + \cdots + 51\!\cdots\!08 T 9 + ⋯ + 5 1 ⋯ 0 8
T^9 - 799*T^8 - 126373*T^7 + 260231615*T^6 - 55666760024*T^5 - 9388800451204*T^4 + 3917560150051472*T^3 - 105835978317839280*T^2 - 64847881643867635840*T + 5198435927658131601408
53 53 5 3
T 9 + ⋯ + 81 ⋯ 24 T^{9} + \cdots + 81\!\cdots\!24 T 9 + ⋯ + 8 1 ⋯ 2 4
T^9 - 780*T^8 + 3046*T^7 + 106276866*T^6 - 20043464110*T^5 - 406316033986*T^4 + 223109745995601*T^3 - 8328427867345954*T^2 + 44441747660879976*T + 81021775771921024
59 59 5 9
T 9 + ⋯ − 11 ⋯ 36 T^{9} + \cdots - 11\!\cdots\!36 T 9 + ⋯ − 1 1 ⋯ 3 6
T^9 - 766*T^8 - 549504*T^7 + 355228158*T^6 + 101161069596*T^5 - 43726722417244*T^4 - 6932524722390463*T^3 + 1213181310743882930*T^2 + 98817384796912108456*T - 11314690678608244580736
61 61 6 1
T 9 + ⋯ − 14 ⋯ 08 T^{9} + \cdots - 14\!\cdots\!08 T 9 + ⋯ − 1 4 ⋯ 0 8
T^9 - 1836*T^8 + 525746*T^7 + 904985476*T^6 - 719048182516*T^5 + 124110189249774*T^4 + 37881163413204019*T^3 - 14400813832577944936*T^2 + 1131274213528450683596*T - 14463046778966443416208
67 67 6 7
T 9 + ⋯ − 44 ⋯ 68 T^{9} + \cdots - 44\!\cdots\!68 T 9 + ⋯ − 4 4 ⋯ 6 8
T^9 + 1290*T^8 - 491345*T^7 - 1224195768*T^6 - 284358128657*T^5 + 203137679469250*T^4 + 79522563930949696*T^3 - 5335043463354907616*T^2 - 4780548879263859441664*T - 446048577911215731898368
71 71 7 1
T 9 + ⋯ − 61 ⋯ 44 T^{9} + \cdots - 61\!\cdots\!44 T 9 + ⋯ − 6 1 ⋯ 4 4
T^9 - 1802*T^8 - 33845*T^7 + 1395092904*T^6 - 420757845917*T^5 - 175009332936274*T^4 + 29666958915556400*T^3 + 6137611121628085856*T^2 - 515366849427733286400*T - 61690004336835389753344
73 73 7 3
T 9 + ⋯ − 91 ⋯ 16 T^{9} + \cdots - 91\!\cdots\!16 T 9 + ⋯ − 9 1 ⋯ 1 6
T^9 - 598*T^8 - 1204620*T^7 + 295166762*T^6 + 413342877519*T^5 - 16910384511468*T^4 - 37136284293297132*T^3 - 342315503780383312*T^2 + 437355806337488967936*T - 9132029472593887638016
79 79 7 9
T 9 + ⋯ + 22 ⋯ 72 T^{9} + \cdots + 22\!\cdots\!72 T 9 + ⋯ + 2 2 ⋯ 7 2
T^9 + 1150*T^8 - 1769316*T^7 - 2245923310*T^6 + 793983575215*T^5 + 1263981768100568*T^4 - 126429388051336692*T^3 - 282921983514589342928*T^2 + 5873031915111544534656*T + 22257566657930532967043072
83 83 8 3
T 9 + ⋯ − 21 ⋯ 68 T^{9} + \cdots - 21\!\cdots\!68 T 9 + ⋯ − 2 1 ⋯ 6 8
T^9 - 1758*T^8 - 205142*T^7 + 1762598860*T^6 - 636375303527*T^5 - 361981679279174*T^4 + 234508391296568684*T^3 - 35650975825734563496*T^2 + 1616202519131705818752*T - 21383935201625945815168
89 89 8 9
T 9 + ⋯ − 11 ⋯ 32 T^{9} + \cdots - 11\!\cdots\!32 T 9 + ⋯ − 1 1 ⋯ 3 2
T^9 - 1400*T^8 - 4034303*T^7 + 5428193002*T^6 + 4593110177763*T^5 - 5810626385285814*T^4 - 1368494445116290056*T^3 + 1614101958554490950352*T^2 - 29410082815615317790544*T - 11732180505787962278478432
97 97 9 7
T 9 + ⋯ − 24 ⋯ 88 T^{9} + \cdots - 24\!\cdots\!88 T 9 + ⋯ − 2 4 ⋯ 8 8
T^9 - 1123*T^8 - 4822578*T^7 + 4544848066*T^6 + 6486537799021*T^5 - 4548648550662335*T^4 - 1700620362043338364*T^3 + 657549285982876847760*T^2 + 104337404629659572170528*T - 24402708276523131149755088
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