[N,k,chi] = [847,4,Mod(1,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("847.1");
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
\(7\)
\(-1\)
\(11\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{4} - 2T_{2}^{3} - 27T_{2}^{2} + 40T_{2} + 112 \)
T2^4 - 2*T2^3 - 27*T2^2 + 40*T2 + 112
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(847))\).
$p$
$F_p(T)$
$2$
\( T^{4} - 2 T^{3} - 27 T^{2} + 40 T + 112 \)
T^4 - 2*T^3 - 27*T^2 + 40*T + 112
$3$
\( T^{4} - 14 T^{3} + 6 T^{2} + \cdots - 1016 \)
T^4 - 14*T^3 + 6*T^2 + 436*T - 1016
$5$
\( T^{4} - 10 T^{3} - 240 T^{2} + \cdots - 4016 \)
T^4 - 10*T^3 - 240*T^2 + 2648*T - 4016
$7$
\( (T - 7)^{4} \)
(T - 7)^4
$11$
\( T^{4} \)
T^4
$13$
\( T^{4} + 58 T^{3} - 4926 T^{2} + \cdots - 4947656 \)
T^4 + 58*T^3 - 4926*T^2 - 342428*T - 4947656
$17$
\( T^{4} + 4 T^{3} - 6186 T^{2} + \cdots - 2705024 \)
T^4 + 4*T^3 - 6186*T^2 - 257456*T - 2705024
$19$
\( T^{4} + 258 T^{3} + \cdots - 14423904 \)
T^4 + 258*T^3 + 16188*T^2 - 161712*T - 14423904
$23$
\( T^{4} - 8 T^{3} - 22392 T^{2} + \cdots - 17449856 \)
T^4 - 8*T^3 - 22392*T^2 + 1550464*T - 17449856
$29$
\( T^{4} - 396 T^{3} + \cdots + 22336464 \)
T^4 - 396*T^3 + 40872*T^2 - 1623888*T + 22336464
$31$
\( T^{4} + 56 T^{3} - 31890 T^{2} + \cdots - 11250248 \)
T^4 + 56*T^3 - 31890*T^2 - 1490896*T - 11250248
$37$
\( T^{4} - 84 T^{3} - 63516 T^{2} + \cdots + 11157312 \)
T^4 - 84*T^3 - 63516*T^2 + 647520*T + 11157312
$41$
\( T^{4} + 52 T^{3} + \cdots - 659233664 \)
T^4 + 52*T^3 - 83706*T^2 - 14752640*T - 659233664
$43$
\( T^{4} + 408 T^{3} + \cdots + 1210397376 \)
T^4 + 408*T^3 - 90804*T^2 - 31826832*T + 1210397376
$47$
\( T^{4} - 8 T^{3} - 121650 T^{2} + \cdots - 318931592 \)
T^4 - 8*T^3 - 121650*T^2 - 12296144*T - 318931592
$53$
\( T^{4} - 624 T^{3} + \cdots + 403923072 \)
T^4 - 624*T^3 + 135948*T^2 - 12426816*T + 403923072
$59$
\( T^{4} + 238 T^{3} + \cdots + 17599820728 \)
T^4 + 238*T^3 - 501426*T^2 - 150381524*T + 17599820728
$61$
\( T^{4} - 162 T^{3} + \cdots + 6668930664 \)
T^4 - 162*T^3 - 587718*T^2 + 166886028*T + 6668930664
$67$
\( T^{4} - 1340 T^{3} + \cdots - 140865466496 \)
T^4 - 1340*T^3 - 172104*T^2 + 658322080*T - 140865466496
$71$
\( T^{4} - 1788 T^{3} + \cdots - 72982082688 \)
T^4 - 1788*T^3 + 761784*T^2 + 109888032*T - 72982082688
$73$
\( T^{4} + 1456 T^{3} + \cdots - 322052228384 \)
T^4 + 1456*T^3 - 388842*T^2 - 1133869160*T - 322052228384
$79$
\( T^{4} - 1324 T^{3} + \cdots - 59537293568 \)
T^4 - 1324*T^3 + 71820*T^2 + 346623968*T - 59537293568
$83$
\( T^{4} + 450 T^{3} + \cdots + 21951092064 \)
T^4 + 450*T^3 - 383316*T^2 - 140617200*T + 21951092064
$89$
\( T^{4} + 3072 T^{3} + \cdots - 109303561968 \)
T^4 + 3072*T^3 + 2868408*T^2 + 704256000*T - 109303561968
$97$
\( T^{4} + 652 T^{3} + \cdots + 868634650768 \)
T^4 + 652*T^3 - 1896360*T^2 - 628130672*T + 868634650768
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