[N,k,chi] = [195,6,Mod(1,195)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(195, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("195.1");
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
3 3 3
+ 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 2 7 − 2 T 2 6 − 201 T 2 5 + 480 T 2 4 + 11274 T 2 3 − 29276 T 2 2 − 162072 T 2 + 455280 T_{2}^{7} - 2T_{2}^{6} - 201T_{2}^{5} + 480T_{2}^{4} + 11274T_{2}^{3} - 29276T_{2}^{2} - 162072T_{2} + 455280 T 2 7 − 2 T 2 6 − 2 0 1 T 2 5 + 4 8 0 T 2 4 + 1 1 2 7 4 T 2 3 − 2 9 2 7 6 T 2 2 − 1 6 2 0 7 2 T 2 + 4 5 5 2 8 0
T2^7 - 2*T2^6 - 201*T2^5 + 480*T2^4 + 11274*T2^3 - 29276*T2^2 - 162072*T2 + 455280
acting on S 6 n e w ( Γ 0 ( 195 ) ) S_{6}^{\mathrm{new}}(\Gamma_0(195)) S 6 n e w ( Γ 0 ( 1 9 5 ) ) .
p p p
F p ( T ) F_p(T) F p ( T )
2 2 2
T 7 − 2 T 6 + ⋯ + 455280 T^{7} - 2 T^{6} + \cdots + 455280 T 7 − 2 T 6 + ⋯ + 4 5 5 2 8 0
T^7 - 2*T^6 - 201*T^5 + 480*T^4 + 11274*T^3 - 29276*T^2 - 162072*T + 455280
3 3 3
( T + 9 ) 7 (T + 9)^{7} ( T + 9 ) 7
(T + 9)^7
5 5 5
( T + 25 ) 7 (T + 25)^{7} ( T + 2 5 ) 7
(T + 25)^7
7 7 7
T 7 + ⋯ + 407345549010432 T^{7} + \cdots + 407345549010432 T 7 + ⋯ + 4 0 7 3 4 5 5 4 9 0 1 0 4 3 2
T^7 - 32*T^6 - 88211*T^5 + 4143266*T^4 + 1995887760*T^3 - 106443927424*T^2 - 7662987230208*T + 407345549010432
11 11 1 1
T 7 + ⋯ + 32 ⋯ 56 T^{7} + \cdots + 32\!\cdots\!56 T 7 + ⋯ + 3 2 ⋯ 5 6
T^7 + 910*T^6 - 452159*T^5 - 627817168*T^4 - 100105600512*T^3 + 47609740670336*T^2 + 12085047769845504*T + 324654137555552256
13 13 1 3
( T − 169 ) 7 (T - 169)^{7} ( T − 1 6 9 ) 7
(T - 169)^7
17 17 1 7
T 7 + ⋯ + 62 ⋯ 44 T^{7} + \cdots + 62\!\cdots\!44 T 7 + ⋯ + 6 2 ⋯ 4 4
T^7 - 142*T^6 - 8486079*T^5 + 2005367224*T^4 + 22666259742696*T^3 - 6652852341589888*T^2 - 19275601794278667120*T + 6262855064282409510144
19 19 1 9
T 7 + ⋯ − 28 ⋯ 40 T^{7} + \cdots - 28\!\cdots\!40 T 7 + ⋯ − 2 8 ⋯ 4 0
T^7 - 2282*T^6 - 7874788*T^5 + 16855841416*T^4 + 13426451537216*T^3 - 17369788069350400*T^2 - 15663175417284384768*T - 2857193185793026826240
23 23 2 3
T 7 + ⋯ + 29 ⋯ 20 T^{7} + \cdots + 29\!\cdots\!20 T 7 + ⋯ + 2 9 ⋯ 2 0
T^7 + 3344*T^6 - 17474963*T^5 - 79179928190*T^4 + 11729094540672*T^3 + 436809456681071872*T^2 + 665775583583701868544*T + 299982862951893067038720
29 29 2 9
T 7 + ⋯ + 35 ⋯ 20 T^{7} + \cdots + 35\!\cdots\!20 T 7 + ⋯ + 3 5 ⋯ 2 0
T^7 + 236*T^6 - 115978532*T^5 + 71968104672*T^4 + 3623107426903536*T^3 - 4362774903224813376*T^2 - 26894552266821698960832*T + 35508123421762507939537920
31 31 3 1
T 7 + ⋯ − 17 ⋯ 16 T^{7} + \cdots - 17\!\cdots\!16 T 7 + ⋯ − 1 7 ⋯ 1 6
T^7 - 6408*T^6 - 130230732*T^5 + 439321309904*T^4 + 6423275678415744*T^3 - 1651053228222446080*T^2 - 103490432434410334563328*T - 176752336430858473769660416
37 37 3 7
T 7 + ⋯ − 48 ⋯ 32 T^{7} + \cdots - 48\!\cdots\!32 T 7 + ⋯ − 4 8 ⋯ 3 2
T^7 + 1732*T^6 - 367323235*T^5 - 676762183098*T^4 + 41644040312727800*T^3 + 98333221581697135408*T^2 - 1484892738724125425804784*T - 4858754899622877023574438432
41 41 4 1
T 7 + ⋯ − 52 ⋯ 04 T^{7} + \cdots - 52\!\cdots\!04 T 7 + ⋯ − 5 2 ⋯ 0 4
T^7 + 10676*T^6 - 360461675*T^5 - 2683517391410*T^4 + 36642824705508408*T^3 + 217897417912769572464*T^2 - 972071577814997965826160*T - 5287781583382564804726579104
43 43 4 3
T 7 + ⋯ + 84 ⋯ 08 T^{7} + \cdots + 84\!\cdots\!08 T 7 + ⋯ + 8 4 ⋯ 0 8
T^7 - 38852*T^6 + 495343328*T^5 - 1300089931136*T^4 - 19964783360869120*T^3 + 151536125762998086656*T^2 - 295487723911572631044096*T + 84681613585092060577988608
47 47 4 7
T 7 + ⋯ + 24 ⋯ 00 T^{7} + \cdots + 24\!\cdots\!00 T 7 + ⋯ + 2 4 ⋯ 0 0
T^7 + 30404*T^6 - 204270012*T^5 - 9665492425216*T^4 + 15214245852424192*T^3 + 758171921775506596864*T^2 - 2764986167658206472867840*T + 2418541130577767062081536000
53 53 5 3
T 7 + ⋯ + 72 ⋯ 64 T^{7} + \cdots + 72\!\cdots\!64 T 7 + ⋯ + 7 2 ⋯ 6 4
T^7 - 21488*T^6 - 836868763*T^5 + 10818926954254*T^4 + 46235652369281976*T^3 - 222547015382387051472*T^2 - 391214701992783452774256*T + 721312431783658582551725664
59 59 5 9
T 7 + ⋯ − 11 ⋯ 28 T^{7} + \cdots - 11\!\cdots\!28 T 7 + ⋯ − 1 1 ⋯ 2 8
T^7 + 13808*T^6 - 3263965824*T^5 - 58419952561280*T^4 + 2675594426104265472*T^3 + 49549836010101602347008*T^2 - 636459944533575171405889536*T - 11364326990085651742005414985728
61 61 6 1
T 7 + ⋯ + 44 ⋯ 08 T^{7} + \cdots + 44\!\cdots\!08 T 7 + ⋯ + 4 4 ⋯ 0 8
T^7 - 110040*T^6 + 951328413*T^5 + 216557350335442*T^4 - 3612340383166494504*T^3 - 157158915057276450506864*T^2 + 1752476376536126060031441296*T + 44169335632603558039313234946208
67 67 6 7
T 7 + ⋯ − 81 ⋯ 12 T^{7} + \cdots - 81\!\cdots\!12 T 7 + ⋯ − 8 1 ⋯ 1 2
T^7 + 28152*T^6 - 5635766384*T^5 - 168361236765184*T^4 + 3739936807291618304*T^3 + 23275019344583726411776*T^2 - 78443209168394342342279168*T - 8106512180458233067073830912
71 71 7 1
T 7 + ⋯ + 57 ⋯ 20 T^{7} + \cdots + 57\!\cdots\!20 T 7 + ⋯ + 5 7 ⋯ 2 0
T^7 - 95122*T^6 - 1189597959*T^5 + 287329449314920*T^4 - 2056958776477600320*T^3 - 250214664518257293967104*T^2 + 2209135077601947836017431552*T + 57633381268961982014463915294720
73 73 7 3
T 7 + ⋯ + 34 ⋯ 52 T^{7} + \cdots + 34\!\cdots\!52 T 7 + ⋯ + 3 4 ⋯ 5 2
T^7 - 2140*T^6 - 4684694916*T^5 - 31704680033728*T^4 + 3970539226678392304*T^3 + 8873756987387873526592*T^2 - 830805080830361441748508608*T + 345161280956152369876750935552
79 79 7 9
T 7 + ⋯ + 26 ⋯ 96 T^{7} + \cdots + 26\!\cdots\!96 T 7 + ⋯ + 2 6 ⋯ 9 6
T^7 + 12046*T^6 - 14646212183*T^5 - 2522014425960*T^4 + 73331290117199531392*T^3 - 818119138080597317999616*T^2 - 125166371571204186182990032896*T + 2676637444320335599456538353565696
83 83 8 3
T 7 + ⋯ − 33 ⋯ 36 T^{7} + \cdots - 33\!\cdots\!36 T 7 + ⋯ − 3 3 ⋯ 3 6
T^7 + 153980*T^6 + 5170239008*T^5 - 208391359791744*T^4 - 12522539810881310464*T^3 - 78025174986584240763904*T^2 + 1449251028452140232598749184*T - 3341576470682061680352356007936
89 89 8 9
T 7 + ⋯ + 20 ⋯ 40 T^{7} + \cdots + 20\!\cdots\!40 T 7 + ⋯ + 2 0 ⋯ 4 0
T^7 + 15252*T^6 - 17132726707*T^5 + 55627224037362*T^4 + 86922817509566693464*T^3 - 1664870189105953144774832*T^2 - 95109354514190244398817493872*T + 2054728991841029627765509684782240
97 97 9 7
T 7 + ⋯ − 28 ⋯ 00 T^{7} + \cdots - 28\!\cdots\!00 T 7 + ⋯ − 2 8 ⋯ 0 0
T^7 + 88554*T^6 - 20629344607*T^5 - 1036199581181280*T^4 + 116148264461987436136*T^3 + 1002306359868361456532032*T^2 - 8245549032669406533257547120*T - 28810101930474347064424546704000
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