[N,k,chi] = [507,8,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, 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("507.1");
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
\(3\)
\(1\)
\(13\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{4} - 6T_{2}^{3} - 441T_{2}^{2} + 2256T_{2} + 6292 \)
T2^4 - 6*T2^3 - 441*T2^2 + 2256*T2 + 6292
acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(507))\).
$p$
$F_p(T)$
$2$
\( T^{4} - 6 T^{3} - 441 T^{2} + \cdots + 6292 \)
T^4 - 6*T^3 - 441*T^2 + 2256*T + 6292
$3$
\( (T + 27)^{4} \)
(T + 27)^4
$5$
\( T^{4} - 276 T^{3} + \cdots + 481985920 \)
T^4 - 276*T^3 - 114712*T^2 + 24189024*T + 481985920
$7$
\( T^{4} - 1116 T^{3} + \cdots + 957942027904 \)
T^4 - 1116*T^3 - 2004808*T^2 + 1281384864*T + 957942027904
$11$
\( T^{4} + \cdots - 198585233297264 \)
T^4 + 4968*T^3 - 46158920*T^2 - 205728922080*T - 198585233297264
$13$
\( T^{4} \)
T^4
$17$
\( T^{4} - 22944 T^{3} + \cdots + 10\!\cdots\!40 \)
T^4 - 22944*T^3 - 853244280*T^2 + 19294734843456*T + 10223281838620240
$19$
\( T^{4} - 26628 T^{3} + \cdots - 62\!\cdots\!88 \)
T^4 - 26628*T^3 - 1735057000*T^2 + 69541775970528*T - 629021411496553088
$23$
\( T^{4} - 23712 T^{3} + \cdots - 81\!\cdots\!00 \)
T^4 - 23712*T^3 - 7942809248*T^2 + 494869775682048*T - 8127296411904300800
$29$
\( T^{4} - 227592 T^{3} + \cdots + 88\!\cdots\!24 \)
T^4 - 227592*T^3 - 6384527144*T^2 + 2109800517520608*T + 88116375608223959824
$31$
\( T^{4} + 531380 T^{3} + \cdots - 14\!\cdots\!04 \)
T^4 + 531380*T^3 + 50194476680*T^2 - 10710985379004896*T - 1461401083466860728704
$37$
\( T^{4} - 630032 T^{3} + \cdots - 88\!\cdots\!16 \)
T^4 - 630032*T^3 - 16702610008*T^2 + 63463946754817280*T - 8880702104587501703216
$41$
\( T^{4} + 212028 T^{3} + \cdots + 32\!\cdots\!28 \)
T^4 + 212028*T^3 - 168260874264*T^2 - 19632053317128096*T + 3295564239068940358528
$43$
\( T^{4} + 1883816 T^{3} + \cdots - 30\!\cdots\!68 \)
T^4 + 1883816*T^3 + 987659405024*T^2 + 57670012389033856*T - 30606336058928972058368
$47$
\( T^{4} - 218976 T^{3} + \cdots + 20\!\cdots\!56 \)
T^4 - 218976*T^3 - 352204677592*T^2 + 57728888839630272*T + 20734125580876600309456
$53$
\( T^{4} - 4469064 T^{3} + \cdots + 87\!\cdots\!96 \)
T^4 - 4469064*T^3 + 6901395170296*T^2 - 4312892039210995872*T + 877615902184484180042896
$59$
\( T^{4} + 6869472 T^{3} + \cdots + 56\!\cdots\!00 \)
T^4 + 6869472*T^3 + 16878857154792*T^2 + 17126256491658343872*T + 5691666739244045692584400
$61$
\( T^{4} - 458456 T^{3} + \cdots + 62\!\cdots\!28 \)
T^4 - 458456*T^3 - 16189093949512*T^2 + 4428754774934053664*T + 62865696631086849910960528
$67$
\( T^{4} - 2218700 T^{3} + \cdots + 16\!\cdots\!24 \)
T^4 - 2218700*T^3 - 8380049891512*T^2 + 16091806528752950048*T + 1677121943565811641476224
$71$
\( T^{4} + 2473128 T^{3} + \cdots + 11\!\cdots\!44 \)
T^4 + 2473128*T^3 - 19954722293864*T^2 - 26441590294105476192*T + 114643329729517942256694544
$73$
\( T^{4} + 10457616 T^{3} + \cdots + 13\!\cdots\!44 \)
T^4 + 10457616*T^3 + 32470975384808*T^2 + 37719048548037279360*T + 13970766905161674022811344
$79$
\( T^{4} - 5130864 T^{3} + \cdots + 21\!\cdots\!08 \)
T^4 - 5130864*T^3 - 40960050137728*T^2 + 179504436835325463552*T + 21201997099738681722769408
$83$
\( T^{4} + 16493520 T^{3} + \cdots - 10\!\cdots\!48 \)
T^4 + 16493520*T^3 + 60358765237896*T^2 - 182539625904851062656*T - 1002781288080977731374070448
$89$
\( T^{4} - 3209484 T^{3} + \cdots + 31\!\cdots\!20 \)
T^4 - 3209484*T^3 - 43321116348616*T^2 + 41751856833713024928*T + 315043333107843851349358720
$97$
\( T^{4} + 17620768 T^{3} + \cdots - 93\!\cdots\!72 \)
T^4 + 17620768*T^3 + 1159436470472*T^2 - 567706728019794814912*T - 93435354115819618146948272
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