[N,k,chi] = [162,9,Mod(161,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.161");
S:= CuspForms(chi, 9);
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
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\)
\(83\)
\(\chi(n)\)
\(-1\)
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
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{8} + 2463336T_{5}^{6} + 2095450167474T_{5}^{4} + 750455927372039400T_{5}^{2} + 96917652743250602030625 \)
T5^8 + 2463336*T5^6 + 2095450167474*T5^4 + 750455927372039400*T5^2 + 96917652743250602030625
acting on \(S_{9}^{\mathrm{new}}(162, [\chi])\).
$p$
$F_p(T)$
$2$
\( (T^{2} + 128)^{4} \)
(T^2 + 128)^4
$3$
\( T^{8} \)
T^8
$5$
\( T^{8} + 2463336 T^{6} + \cdots + 96\!\cdots\!25 \)
T^8 + 2463336*T^6 + 2095450167474*T^4 + 750455927372039400*T^2 + 96917652743250602030625
$7$
\( (T^{4} + 4438 T^{3} + \cdots - 4511860509296)^{2} \)
(T^4 + 4438*T^3 + 1714902*T^2 - 8443400504*T - 4511860509296)^2
$11$
\( T^{8} + 1083686796 T^{6} + \cdots + 28\!\cdots\!84 \)
T^8 + 1083686796*T^6 + 317317413185164548*T^4 + 20353226100360123126578112*T^2 + 283502639123119297793119338825984
$13$
\( (T^{4} + 58690 T^{3} + \cdots - 168608080827623)^{2} \)
(T^4 + 58690*T^3 + 217031802*T^2 - 635220433094*T - 168608080827623)^2
$17$
\( T^{8} + 40156998768 T^{6} + \cdots + 42\!\cdots\!25 \)
T^8 + 40156998768*T^6 + 510294988222009429194*T^4 + 2551959865925208891419031003600*T^2 + 4217922726617712896411099227720420505625
$19$
\( (T^{4} - 135110 T^{3} + \cdots + 27\!\cdots\!24)^{2} \)
(T^4 - 135110*T^3 - 35679757458*T^2 + 3116993336273560*T + 270942855587702179024)^2
$23$
\( T^{8} + 283534373268 T^{6} + \cdots + 21\!\cdots\!00 \)
T^8 + 283534373268*T^6 + 24108135163800112732356*T^4 + 553546115769303825530004683121600*T^2 + 2123618993531056655010196460165109313440000
$29$
\( T^{8} + 1677572170848 T^{6} + \cdots + 31\!\cdots\!89 \)
T^8 + 1677572170848*T^6 + 803713838208314050995642*T^4 + 81176598470995210382047214290608384*T^2 + 314842342520759388807252293178196159270514889
$31$
\( (T^{4} + 196672 T^{3} + \cdots + 54\!\cdots\!96)^{2} \)
(T^4 + 196672*T^3 - 1740567617580*T^2 - 902876154259404992*T + 54393820421175534704896)^2
$37$
\( (T^{4} - 915494 T^{3} + \cdots + 16\!\cdots\!21)^{2} \)
(T^4 - 915494*T^3 - 759687273030*T^2 + 325892367842531098*T + 169705141882753595724721)^2
$41$
\( T^{8} + 42402792363120 T^{6} + \cdots + 10\!\cdots\!96 \)
T^8 + 42402792363120*T^6 + 482228326894441943339778456*T^4 + 1315293101907265881399900069683211067200*T^2 + 108371387804547404061075910600945730552447250807696
$43$
\( (T^{4} - 5567618 T^{3} + \cdots - 13\!\cdots\!64)^{2} \)
(T^4 - 5567618*T^3 - 19502735997810*T^2 + 121179016074751370824*T - 135781037741657030982876464)^2
$47$
\( T^{8} + 62658471632112 T^{6} + \cdots + 21\!\cdots\!96 \)
T^8 + 62658471632112*T^6 + 692312405345361140833771920*T^4 + 2299741902247305026028866667356337435648*T^2 + 2139183940888601104228429532964016845418671976759296
$53$
\( T^{8} + 288880676034192 T^{6} + \cdots + 47\!\cdots\!24 \)
T^8 + 288880676034192*T^6 + 24766367974760329339098393432*T^4 + 635901595355570574140352053442089073895104*T^2 + 4790607658639006626548382017665315688389600666579707024
$59$
\( T^{8} + 85968765926928 T^{6} + \cdots + 11\!\cdots\!24 \)
T^8 + 85968765926928*T^6 + 2451017308500271427964041232*T^4 + 28376752878969841301984420590787814061056*T^2 + 115320449756057752538132921521146294534282665692237824
$61$
\( (T^{4} - 6092102 T^{3} + \cdots + 12\!\cdots\!01)^{2} \)
(T^4 - 6092102*T^3 - 307916182938450*T^2 + 2576943458245767370162*T + 122608426199279579831804701)^2
$67$
\( (T^{4} + 40177858 T^{3} + \cdots - 44\!\cdots\!32)^{2} \)
(T^4 + 40177858*T^3 + 207581168227686*T^2 - 5878915098038704345064*T - 44487453244000249876463346032)^2
$71$
\( T^{8} + \cdots + 34\!\cdots\!76 \)
T^8 + 2209145704295796*T^6 + 1133524571451859786455272008260*T^4 + 49800583475507006572253443514738912701866816*T^2 + 348736183777095791574536775702362547990108316445054443776
$73$
\( (T^{4} - 98542880 T^{3} + \cdots - 56\!\cdots\!27)^{2} \)
(T^4 - 98542880*T^3 + 2492847039328530*T^2 + 6094902148672064924128*T - 569154726207587263839484542527)^2
$79$
\( (T^{4} - 42225926 T^{3} + \cdots + 52\!\cdots\!92)^{2} \)
(T^4 - 42225926*T^3 - 4554049357168914*T^2 + 116346452265503356382824*T + 5247853214672320354348399243792)^2
$83$
\( T^{8} + \cdots + 15\!\cdots\!44 \)
T^8 + 11030368811799888*T^6 + 28272129139940078463528547490112*T^4 + 20404829722897232542891307378213597013352759296*T^2 + 1513917008478344395807908556110902423981015992050943158534144
$89$
\( T^{8} + \cdots + 39\!\cdots\!61 \)
T^8 + 19102894897778136*T^6 + 116985980241221131098837395305362*T^4 + 231001739102081560170529710694012480461502829784*T^2 + 39114396464277127150378977387520979575993697541446654766916161
$97$
\( (T^{4} - 170568464 T^{3} + \cdots - 41\!\cdots\!32)^{2} \)
(T^4 - 170568464*T^3 - 8882551209578412*T^2 + 2073924445074562601223232*T - 41759447146241335661464840408832)^2
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