[N,k,chi] = [276,6,Mod(1,276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(276, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("276.1");
S:= CuspForms(chi, 6);
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
\(2\)
\(-1\)
\(3\)
\(-1\)
\(23\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{4} + 50T_{5}^{3} - 3132T_{5}^{2} - 30400T_{5} - 25344 \)
T5^4 + 50*T5^3 - 3132*T5^2 - 30400*T5 - 25344
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(276))\).
$p$
$F_p(T)$
$2$
\( T^{4} \)
T^4
$3$
\( (T - 9)^{4} \)
(T - 9)^4
$5$
\( T^{4} + 50 T^{3} - 3132 T^{2} + \cdots - 25344 \)
T^4 + 50*T^3 - 3132*T^2 - 30400*T - 25344
$7$
\( T^{4} + 62 T^{3} - 31216 T^{2} + \cdots + 79217776 \)
T^4 + 62*T^3 - 31216*T^2 - 1472248*T + 79217776
$11$
\( T^{4} + 392 T^{3} + \cdots - 3025951488 \)
T^4 + 392*T^3 - 257936*T^2 - 101637760*T - 3025951488
$13$
\( T^{4} + 396 T^{3} + \cdots - 140168104144 \)
T^4 + 396*T^3 - 1004592*T^2 - 751917936*T - 140168104144
$17$
\( T^{4} + 794 T^{3} + \cdots - 553461499200 \)
T^4 + 794*T^3 - 2769508*T^2 - 2624978384*T - 553461499200
$19$
\( T^{4} + 374 T^{3} + \cdots + 2403073414064 \)
T^4 + 374*T^3 - 4080600*T^2 + 396212344*T + 2403073414064
$23$
\( (T + 529)^{4} \)
(T + 529)^4
$29$
\( T^{4} + 10028 T^{3} + \cdots + 10508867384496 \)
T^4 + 10028*T^3 + 34398256*T^2 + 43445628560*T + 10508867384496
$31$
\( T^{4} + \cdots - 677576433888000 \)
T^4 + 7092*T^3 - 38460704*T^2 - 377297207104*T - 677576433888000
$37$
\( T^{4} + 16436 T^{3} + \cdots + 12\!\cdots\!16 \)
T^4 + 16436*T^3 - 11984368*T^2 - 660613356304*T + 1235497552999216
$41$
\( T^{4} + \cdots - 933488207082288 \)
T^4 + 20384*T^3 + 81509800*T^2 - 278189262912*T - 933488207082288
$43$
\( T^{4} + 18206 T^{3} + \cdots - 71181372294800 \)
T^4 + 18206*T^3 + 83050888*T^2 + 89470026040*T - 71181372294800
$47$
\( T^{4} + \cdots - 250538124570624 \)
T^4 + 30872*T^3 + 83272912*T^2 - 1148053329408*T - 250538124570624
$53$
\( T^{4} + \cdots - 212742156308160 \)
T^4 + 11150*T^3 - 95290100*T^2 - 323102512864*T - 212742156308160
$59$
\( T^{4} + 16080 T^{3} + \cdots + 22\!\cdots\!40 \)
T^4 + 16080*T^3 - 909384656*T^2 - 7338209780736*T + 225860707095229440
$61$
\( T^{4} - 156 T^{3} + \cdots + 86\!\cdots\!24 \)
T^4 - 156*T^3 - 434773104*T^2 - 695822823888*T + 8627756436997424
$67$
\( T^{4} + 12122 T^{3} + \cdots + 14\!\cdots\!20 \)
T^4 + 12122*T^3 - 1058803592*T^2 - 7283285603544*T + 144553583247401520
$71$
\( T^{4} + 69840 T^{3} + \cdots - 10\!\cdots\!68 \)
T^4 + 69840*T^3 + 289002688*T^2 - 63748185553920*T - 1095285166821715968
$73$
\( T^{4} - 3008 T^{3} + \cdots + 31\!\cdots\!48 \)
T^4 - 3008*T^3 - 4965000536*T^2 + 36270287236672*T + 3127363255186020048
$79$
\( T^{4} + 106522 T^{3} + \cdots - 57\!\cdots\!40 \)
T^4 + 106522*T^3 - 1698088976*T^2 - 376217703403304*T - 5792480564649012240
$83$
\( T^{4} + 137928 T^{3} + \cdots - 21\!\cdots\!68 \)
T^4 + 137928*T^3 - 2978385776*T^2 - 795390715443200*T - 21214960977191232768
$89$
\( T^{4} + 121878 T^{3} + \cdots - 44\!\cdots\!00 \)
T^4 + 121878*T^3 - 1225545404*T^2 - 100260171243216*T - 44894935528660800
$97$
\( T^{4} + 100956 T^{3} + \cdots + 33\!\cdots\!52 \)
T^4 + 100956*T^3 - 15947406272*T^2 - 447343428388144*T + 33155707909435523952
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