[N,k,chi] = [667,2,Mod(1,667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(667, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("667.1");
S:= CuspForms(chi, 2);
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
\( p \)
Sign
\(23\)
\(1\)
\(29\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{12} + 3 T_{2}^{11} - 13 T_{2}^{10} - 41 T_{2}^{9} + 54 T_{2}^{8} + 188 T_{2}^{7} - 77 T_{2}^{6} - 342 T_{2}^{5} + 13 T_{2}^{4} + 215 T_{2}^{3} + 9 T_{2}^{2} - 37 T_{2} - 5 \)
T2^12 + 3*T2^11 - 13*T2^10 - 41*T2^9 + 54*T2^8 + 188*T2^7 - 77*T2^6 - 342*T2^5 + 13*T2^4 + 215*T2^3 + 9*T2^2 - 37*T2 - 5
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(667))\).
$p$
$F_p(T)$
$2$
\( T^{12} + 3 T^{11} - 13 T^{10} - 41 T^{9} + \cdots - 5 \)
T^12 + 3*T^11 - 13*T^10 - 41*T^9 + 54*T^8 + 188*T^7 - 77*T^6 - 342*T^5 + 13*T^4 + 215*T^3 + 9*T^2 - 37*T - 5
$3$
\( T^{12} + 3 T^{11} - 15 T^{10} - 44 T^{9} + \cdots - 1 \)
T^12 + 3*T^11 - 15*T^10 - 44*T^9 + 74*T^8 + 207*T^7 - 150*T^6 - 382*T^5 + 129*T^4 + 256*T^3 - 48*T^2 - 46*T - 1
$5$
\( T^{12} + 16 T^{11} + 91 T^{10} + \cdots + 583 \)
T^12 + 16*T^11 + 91*T^10 + 162*T^9 - 396*T^8 - 1943*T^7 - 1627*T^6 + 2991*T^5 + 4808*T^4 - 660*T^3 - 3214*T^2 - 300*T + 583
$7$
\( T^{12} + 7 T^{11} - 19 T^{10} - 182 T^{9} + \cdots - 16 \)
T^12 + 7*T^11 - 19*T^10 - 182*T^9 + 125*T^8 + 1631*T^7 - 741*T^6 - 5425*T^5 + 3679*T^4 + 1988*T^3 - 413*T^2 - 216*T - 16
$11$
\( T^{12} + 6 T^{11} - 63 T^{10} + \cdots + 266075 \)
T^12 + 6*T^11 - 63*T^10 - 443*T^9 + 1046*T^8 + 11450*T^7 + 4140*T^6 - 115816*T^5 - 213703*T^4 + 279150*T^3 + 1146714*T^2 + 1063507*T + 266075
$13$
\( T^{12} + 15 T^{11} + 10 T^{10} + \cdots + 3090655 \)
T^12 + 15*T^11 + 10*T^10 - 872*T^9 - 3802*T^8 + 12082*T^7 + 102285*T^6 + 42364*T^5 - 915400*T^4 - 1602192*T^3 + 2072413*T^2 + 6460857*T + 3090655
$17$
\( T^{12} + 18 T^{11} + 71 T^{10} + \cdots - 9596 \)
T^12 + 18*T^11 + 71*T^10 - 436*T^9 - 3484*T^8 - 1682*T^7 + 31076*T^6 + 39627*T^5 - 91550*T^4 - 103277*T^3 + 67893*T^2 + 31240*T - 9596
$19$
\( T^{12} + 6 T^{11} - 119 T^{10} + \cdots - 149440 \)
T^12 + 6*T^11 - 119*T^10 - 897*T^9 + 3160*T^8 + 38666*T^7 + 43638*T^6 - 400570*T^5 - 1308005*T^4 - 870280*T^3 + 1241085*T^2 + 1324256*T - 149440
$23$
\( (T + 1)^{12} \)
(T + 1)^12
$29$
\( (T + 1)^{12} \)
(T + 1)^12
$31$
\( T^{12} - 16 T^{11} + 25 T^{10} + \cdots + 169 \)
T^12 - 16*T^11 + 25*T^10 + 703*T^9 - 3333*T^8 - 4023*T^7 + 52027*T^6 - 90550*T^5 - 8705*T^4 + 97636*T^3 - 13018*T^2 - 29220*T + 169
$37$
\( T^{12} + T^{11} - 300 T^{10} + \cdots - 362875340 \)
T^12 + T^11 - 300*T^10 - 139*T^9 + 32317*T^8 - 12921*T^7 - 1538543*T^6 + 2097862*T^5 + 29813443*T^4 - 67960955*T^3 - 132885771*T^2 + 492689776*T - 362875340
$41$
\( T^{12} - 3 T^{11} - 225 T^{10} + \cdots - 27754352 \)
T^12 - 3*T^11 - 225*T^10 + 100*T^9 + 19334*T^8 + 36992*T^7 - 688351*T^6 - 2820556*T^5 + 5620365*T^4 + 51050139*T^3 + 95038325*T^2 + 39955432*T - 27754352
$43$
\( T^{12} + 23 T^{11} + \cdots - 229352509 \)
T^12 + 23*T^11 + 18*T^10 - 3715*T^9 - 34372*T^8 - 4348*T^7 + 1432697*T^6 + 7019312*T^5 + 120819*T^4 - 98139927*T^3 - 332516092*T^2 - 456409123*T - 229352509
$47$
\( T^{12} + 35 T^{11} + 222 T^{10} + \cdots - 40804117 \)
T^12 + 35*T^11 + 222*T^10 - 5007*T^9 - 68952*T^8 + 22788*T^7 + 4020829*T^6 + 14545371*T^5 - 32908165*T^4 - 139288371*T^3 + 195233100*T^2 - 3930358*T - 40804117
$53$
\( T^{12} + 45 T^{11} + \cdots - 142956229 \)
T^12 + 45*T^11 + 683*T^10 + 1491*T^9 - 74630*T^8 - 947515*T^7 - 4586185*T^6 - 4447789*T^5 + 43362431*T^4 + 155347564*T^3 + 103125523*T^2 - 192812894*T - 142956229
$59$
\( T^{12} + 11 T^{11} + \cdots + 8891929600 \)
T^12 + 11*T^11 - 386*T^10 - 3752*T^9 + 56094*T^8 + 472329*T^7 - 3722991*T^6 - 27279008*T^5 + 110629045*T^4 + 690028123*T^3 - 1293585763*T^2 - 5050998336*T + 8891929600
$61$
\( T^{12} - 4 T^{11} - 288 T^{10} + \cdots - 18119916 \)
T^12 - 4*T^11 - 288*T^10 + 1218*T^9 + 23370*T^8 - 90746*T^7 - 674995*T^6 + 2446190*T^5 + 6151210*T^4 - 22849850*T^3 + 5427069*T^2 + 27947196*T - 18119916
$67$
\( T^{12} + 19 T^{11} + \cdots - 409376228 \)
T^12 + 19*T^11 - 222*T^10 - 5505*T^9 + 10401*T^8 + 575866*T^7 + 841992*T^6 - 25317130*T^5 - 86438366*T^4 + 354520568*T^3 + 1996739575*T^2 + 2093598060*T - 409376228
$71$
\( T^{12} - 19 T^{11} + \cdots - 226642180 \)
T^12 - 19*T^11 - 295*T^10 + 6170*T^9 + 24172*T^8 - 560972*T^7 - 1037483*T^6 + 17462558*T^5 + 12049787*T^4 - 184276655*T^3 + 107691351*T^2 + 276404288*T - 226642180
$73$
\( T^{12} - 10 T^{11} + \cdots + 2131153580 \)
T^12 - 10*T^11 - 406*T^10 + 2423*T^9 + 68014*T^8 - 113916*T^7 - 5196543*T^6 - 8381771*T^5 + 138848386*T^4 + 468676890*T^3 - 522062685*T^2 - 2044166852*T + 2131153580
$79$
\( T^{12} - 17 T^{11} - 222 T^{10} + \cdots - 36136523 \)
T^12 - 17*T^11 - 222*T^10 + 5302*T^9 - 2683*T^8 - 410928*T^7 + 1741621*T^6 + 6564553*T^5 - 42217641*T^4 + 8905014*T^3 + 115383457*T^2 + 19569650*T - 36136523
$83$
\( T^{12} + 12 T^{11} + \cdots + 14844146512 \)
T^12 + 12*T^11 - 638*T^10 - 4819*T^9 + 153191*T^8 + 220621*T^7 - 16696731*T^6 + 68049836*T^5 + 446283618*T^4 - 4686902763*T^3 + 16164213229*T^2 - 25209439576*T + 14844146512
$89$
\( T^{12} + 20 T^{11} + \cdots - 12272416784 \)
T^12 + 20*T^11 - 384*T^10 - 9078*T^9 + 35172*T^8 + 1362447*T^7 + 1332308*T^6 - 76569835*T^5 - 227836659*T^4 + 1422097864*T^3 + 5874747827*T^2 - 453908952*T - 12272416784
$97$
\( T^{12} + 12 T^{11} + \cdots - 6155578420 \)
T^12 + 12*T^11 - 368*T^10 - 5224*T^9 + 33165*T^8 + 648971*T^7 - 422404*T^6 - 31011322*T^5 - 42211711*T^4 + 559443202*T^3 + 1049161983*T^2 - 3227158204*T - 6155578420
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