[N,k,chi] = [460,4,Mod(1,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, 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("460.1");
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 \(\iota_m\) 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
\(2\)
\(-1\)
\(5\)
\(-1\)
\(23\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{5} + 7T_{3}^{4} - 58T_{3}^{3} - 385T_{3}^{2} + 123T_{3} + 12 \)
T3^5 + 7*T3^4 - 58*T3^3 - 385*T3^2 + 123*T3 + 12
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(460))\).
$p$
$F_p(T)$
$2$
\( T^{5} \)
T^5
$3$
\( T^{5} + 7 T^{4} - 58 T^{3} - 385 T^{2} + \cdots + 12 \)
T^5 + 7*T^4 - 58*T^3 - 385*T^2 + 123*T + 12
$5$
\( (T - 5)^{5} \)
(T - 5)^5
$7$
\( T^{5} + 20 T^{4} - 576 T^{3} + \cdots + 270924 \)
T^5 + 20*T^4 - 576*T^3 - 12437*T^2 - 7210*T + 270924
$11$
\( T^{5} + 63 T^{4} - 1803 T^{3} + \cdots + 72719208 \)
T^5 + 63*T^4 - 1803*T^3 - 144540*T^2 + 394848*T + 72719208
$13$
\( T^{5} + 99 T^{4} - 1576 T^{3} + \cdots - 14392890 \)
T^5 + 99*T^4 - 1576*T^3 - 260553*T^2 - 3747573*T - 14392890
$17$
\( T^{5} + 44 T^{4} + \cdots + 451144080 \)
T^5 + 44*T^4 - 11356*T^3 - 230129*T^2 + 24129612*T + 451144080
$19$
\( T^{5} + 199 T^{4} + \cdots - 800499864 \)
T^5 + 199*T^4 - 4473*T^3 - 2422460*T^2 - 102482384*T - 800499864
$23$
\( (T - 23)^{5} \)
(T - 23)^5
$29$
\( T^{5} - 231 T^{4} + \cdots + 43256062404 \)
T^5 - 231*T^4 - 43347*T^3 + 16885475*T^2 - 1571608782*T + 43256062404
$31$
\( T^{5} + 518 T^{4} + \cdots - 9011869285 \)
T^5 + 518*T^4 + 91393*T^3 + 5651171*T^2 - 26022014*T - 9011869285
$37$
\( T^{5} + 113 T^{4} + \cdots - 409221703936 \)
T^5 + 113*T^4 - 200066*T^3 - 11945668*T^2 + 8756657824*T - 409221703936
$41$
\( T^{5} + 174 T^{4} + \cdots + 12760146261 \)
T^5 + 174*T^4 - 65373*T^3 - 1600019*T^2 + 552958956*T + 12760146261
$43$
\( T^{5} + 298 T^{4} + \cdots + 803496865792 \)
T^5 + 298*T^4 - 206636*T^3 - 35638736*T^2 + 10450590016*T + 803496865792
$47$
\( T^{5} + 360 T^{4} + \cdots + 13556115821808 \)
T^5 + 360*T^4 - 460803*T^3 - 139482110*T^2 + 51971864940*T + 13556115821808
$53$
\( T^{5} - 217 T^{4} + \cdots - 4075860543408 \)
T^5 - 217*T^4 - 425172*T^3 + 67682736*T^2 + 32009178240*T - 4075860543408
$59$
\( T^{5} + 1551 T^{4} + \cdots - 897857553600 \)
T^5 + 1551*T^4 + 776914*T^3 + 132858756*T^2 + 610600000*T - 897857553600
$61$
\( T^{5} + 737 T^{4} + \cdots + 310836562128 \)
T^5 + 737*T^4 - 143617*T^3 - 54652610*T^2 + 1001656572*T + 310836562128
$67$
\( T^{5} + \cdots + 137714931264960 \)
T^5 + 539*T^4 - 1191554*T^3 - 685851228*T^2 + 239493222816*T + 137714931264960
$71$
\( T^{5} + \cdots - 108175489939041 \)
T^5 + 1736*T^4 + 309825*T^3 - 963200923*T^2 - 625080224750*T - 108175489939041
$73$
\( T^{5} + 628 T^{4} + \cdots + 13803900176376 \)
T^5 + 628*T^4 - 854841*T^3 - 232147504*T^2 + 125277344960*T + 13803900176376
$79$
\( T^{5} + 2954 T^{4} + \cdots - 8954177264640 \)
T^5 + 2954*T^4 + 3008564*T^3 + 1204381504*T^2 + 140317876032*T - 8954177264640
$83$
\( T^{5} + 153 T^{4} + \cdots - 29112932977344 \)
T^5 + 153*T^4 - 2153688*T^3 + 117021020*T^2 + 410651494416*T - 29112932977344
$89$
\( T^{5} + \cdots + 180704830832640 \)
T^5 + 1558*T^4 - 2008764*T^3 - 4508115456*T^2 - 1753065715968*T + 180704830832640
$97$
\( T^{5} + \cdots + 347840565067560 \)
T^5 + 1375*T^4 - 2138463*T^3 - 2498855432*T^2 + 861720681064*T + 347840565067560
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