[N,k,chi] = [33,8,Mod(1,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.1");
S:= CuspForms(chi, 8);
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
\(3\)
\(-1\)
\(11\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{4} - 15T_{2}^{3} - 426T_{2}^{2} + 5416T_{2} + 14736 \)
T2^4 - 15*T2^3 - 426*T2^2 + 5416*T2 + 14736
acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(33))\).
$p$
$F_p(T)$
$2$
\( T^{4} - 15 T^{3} - 426 T^{2} + \cdots + 14736 \)
T^4 - 15*T^3 - 426*T^2 + 5416*T + 14736
$3$
\( (T - 27)^{4} \)
(T - 27)^4
$5$
\( T^{4} - 306 T^{3} + \cdots + 1251456000 \)
T^4 - 306*T^3 - 145860*T^2 + 41897800*T + 1251456000
$7$
\( T^{4} - 890 T^{3} + \cdots + 69611139776 \)
T^4 - 890*T^3 - 865524*T^2 + 685761128*T + 69611139776
$11$
\( (T - 1331)^{4} \)
(T - 1331)^4
$13$
\( T^{4} + \cdots - 161846909982208 \)
T^4 + 1822*T^3 - 107560020*T^2 + 400331747816*T - 161846909982208
$17$
\( T^{4} - 32856 T^{3} + \cdots + 16\!\cdots\!76 \)
T^4 - 32856*T^3 - 23660052*T^2 + 4865986045216*T + 16067809802621376
$19$
\( T^{4} + 12784 T^{3} + \cdots + 43\!\cdots\!00 \)
T^4 + 12784*T^3 - 1606627884*T^2 + 13513977630000*T + 43343851194000000
$23$
\( T^{4} - 114858 T^{3} + \cdots - 49\!\cdots\!52 \)
T^4 - 114858*T^3 - 4013590032*T^2 + 575158447385600*T - 4903263376549527552
$29$
\( T^{4} + 104952 T^{3} + \cdots + 66\!\cdots\!00 \)
T^4 + 104952*T^3 - 16791650964*T^2 - 1254405448966464*T + 66190358153413958400
$31$
\( T^{4} + 24976 T^{3} + \cdots + 59\!\cdots\!52 \)
T^4 + 24976*T^3 - 66361664448*T^2 + 677650700638208*T + 596061149141131722752
$37$
\( T^{4} + 498856 T^{3} + \cdots + 37\!\cdots\!72 \)
T^4 + 498856*T^3 + 2249707560*T^2 - 9552703697159328*T + 37650528935713153872
$41$
\( T^{4} - 734556 T^{3} + \cdots - 49\!\cdots\!64 \)
T^4 - 734556*T^3 - 196473342828*T^2 + 255101111276933824*T - 49145490407336028881664
$43$
\( T^{4} + 201916 T^{3} + \cdots - 18\!\cdots\!00 \)
T^4 + 201916*T^3 - 750237599340*T^2 - 333752463260764416*T - 18950215213957699425600
$47$
\( T^{4} - 1995894 T^{3} + \cdots - 25\!\cdots\!76 \)
T^4 - 1995894*T^3 + 515393951520*T^2 + 677068295056728704*T - 253896068610010195378176
$53$
\( T^{4} - 929970 T^{3} + \cdots - 80\!\cdots\!56 \)
T^4 - 929970*T^3 - 4002003211716*T^2 + 3687821737137975528*T - 804967176398076162622656
$59$
\( T^{4} - 1353156 T^{3} + \cdots + 12\!\cdots\!40 \)
T^4 - 1353156*T^3 - 9313188846576*T^2 + 9464513206675985216*T + 12780262609967146886423040
$61$
\( T^{4} - 3998774 T^{3} + \cdots - 13\!\cdots\!48 \)
T^4 - 3998774*T^3 + 3631506281556*T^2 + 892807921807965720*T - 1352091678741407087559648
$67$
\( T^{4} - 1722008 T^{3} + \cdots - 15\!\cdots\!96 \)
T^4 - 1722008*T^3 - 1598346829632*T^2 - 297745381766908544*T - 15097516695340836797696
$71$
\( T^{4} - 5571858 T^{3} + \cdots - 50\!\cdots\!80 \)
T^4 - 5571858*T^3 + 428757625584*T^2 + 38744354437683831936*T - 50700766303905834613754880
$73$
\( T^{4} - 5600528 T^{3} + \cdots + 45\!\cdots\!12 \)
T^4 - 5600528*T^3 - 3592938391656*T^2 + 778267153014592064*T + 458603037690886743642512
$79$
\( T^{4} + 7710226 T^{3} + \cdots - 88\!\cdots\!40 \)
T^4 + 7710226*T^3 + 15365889919788*T^2 - 135860409256235432*T - 8863254922791986255690240
$83$
\( T^{4} - 3431856 T^{3} + \cdots + 11\!\cdots\!72 \)
T^4 - 3431856*T^3 - 64786574103120*T^2 + 189944581820061777408*T + 11232074892435416437174272
$89$
\( T^{4} - 4611528 T^{3} + \cdots - 11\!\cdots\!60 \)
T^4 - 4611528*T^3 - 26649980481960*T^2 + 143448626454713314272*T - 115665373518056983939883760
$97$
\( T^{4} - 1401692 T^{3} + \cdots - 11\!\cdots\!36 \)
T^4 - 1401692*T^3 - 153686368066368*T^2 - 826948266905717998736*T - 1167447505500746420363441936
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