[N,k,chi] = [123,4,Mod(1,123)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(123, 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("123.1");
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
\(3\)
\(-1\)
\(41\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{6} - 6T_{2}^{5} - 19T_{2}^{4} + 142T_{2}^{3} + 2T_{2}^{2} - 588T_{2} + 196 \)
T2^6 - 6*T2^5 - 19*T2^4 + 142*T2^3 + 2*T2^2 - 588*T2 + 196
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(123))\).
$p$
$F_p(T)$
$2$
\( T^{6} - 6 T^{5} - 19 T^{4} + 142 T^{3} + \cdots + 196 \)
T^6 - 6*T^5 - 19*T^4 + 142*T^3 + 2*T^2 - 588*T + 196
$3$
\( (T - 3)^{6} \)
(T - 3)^6
$5$
\( T^{6} - 37 T^{5} + 190 T^{4} + \cdots + 1135256 \)
T^6 - 37*T^5 + 190*T^4 + 5484*T^3 - 49732*T^2 - 83596*T + 1135256
$7$
\( T^{6} - 14 T^{5} - 636 T^{4} + \cdots + 2293568 \)
T^6 - 14*T^5 - 636*T^4 + 12944*T^3 - 27732*T^2 - 534472*T + 2293568
$11$
\( T^{6} - 50 T^{5} - 4014 T^{4} + \cdots - 81911864 \)
T^6 - 50*T^5 - 4014*T^4 + 149112*T^3 + 3092249*T^2 - 13673446*T - 81911864
$13$
\( T^{6} - 27 T^{5} + \cdots - 978161912 \)
T^6 - 27*T^5 - 4406*T^4 + 84012*T^3 + 3877836*T^2 - 32975332*T - 978161912
$17$
\( T^{6} - 43 T^{5} + \cdots + 19797717802 \)
T^6 - 43*T^5 - 16880*T^4 + 803486*T^3 + 61815689*T^2 - 3476604263*T + 19797717802
$19$
\( T^{6} - 111 T^{5} + \cdots + 1289742832 \)
T^6 - 111*T^5 - 8816*T^4 + 1077252*T^3 - 15777852*T^2 - 401403092*T + 1289742832
$23$
\( T^{6} - 294 T^{5} + \cdots + 50890186048 \)
T^6 - 294*T^5 + 8660*T^4 + 2263952*T^3 - 72244852*T^2 - 4788465864*T + 50890186048
$29$
\( T^{6} - 234 T^{5} + \cdots + 2531498501216 \)
T^6 - 234*T^5 - 61126*T^4 + 22517376*T^3 - 1863065271*T^2 + 4762364554*T + 2531498501216
$31$
\( T^{6} + 121 T^{5} + \cdots - 2218959458272 \)
T^6 + 121*T^5 - 59390*T^4 - 3035238*T^3 + 827347517*T^2 + 11929806349*T - 2218959458272
$37$
\( T^{6} + 28 T^{5} + \cdots + 884867511276 \)
T^6 + 28*T^5 - 62238*T^4 + 5249828*T^3 + 249305721*T^2 - 36295278840*T + 884867511276
$41$
\( (T - 41)^{6} \)
(T - 41)^6
$43$
\( T^{6} + 492 T^{5} + \cdots - 17814848169328 \)
T^6 + 492*T^5 - 58154*T^4 - 37622364*T^3 - 172064511*T^2 + 451211385816*T - 17814848169328
$47$
\( T^{6} + 280 T^{5} + \cdots + 96987904976768 \)
T^6 + 280*T^5 - 311438*T^4 - 89010636*T^3 + 12082758433*T^2 + 2935400102908*T + 96987904976768
$53$
\( T^{6} + \cdots - 270637221082112 \)
T^6 - 472*T^5 - 255124*T^4 + 78893088*T^3 + 19897594304*T^2 - 2512089573376*T - 270637221082112
$59$
\( T^{6} + \cdots - 586668983577344 \)
T^6 - 595*T^5 - 711148*T^4 + 411206448*T^3 + 45929488896*T^2 - 19233993645632*T - 586668983577344
$61$
\( T^{6} + \cdots - 499608027642676 \)
T^6 + 468*T^5 - 492558*T^4 - 165714660*T^3 + 61322008937*T^2 + 10832325901032*T - 499608027642676
$67$
\( T^{6} + \cdots - 869522980253504 \)
T^6 + 335*T^5 - 907452*T^4 - 349576728*T^3 + 34269867184*T^2 + 14070692665008*T - 869522980253504
$71$
\( T^{6} - 753 T^{5} + \cdots + 12\!\cdots\!48 \)
T^6 - 753*T^5 - 571050*T^4 + 546262634*T^3 - 17093559475*T^2 - 66087065056661*T + 12462875520270248
$73$
\( T^{6} + \cdots - 420232761125654 \)
T^6 + 1177*T^5 + 235324*T^4 - 144776254*T^3 - 67092760247*T^2 - 9344192081355*T - 420232761125654
$79$
\( T^{6} + \cdots - 822986137536512 \)
T^6 + 612*T^5 - 794872*T^4 - 350530336*T^3 + 134545592144*T^2 + 8938755283776*T - 822986137536512
$83$
\( T^{6} - 1919 T^{5} + \cdots + 41\!\cdots\!88 \)
T^6 - 1919*T^5 + 233856*T^4 + 951338484*T^3 - 429335556476*T^2 + 30546664133868*T + 4171347785223088
$89$
\( T^{6} - 2659 T^{5} + \cdots - 65\!\cdots\!48 \)
T^6 - 2659*T^5 + 637546*T^4 + 2345835176*T^3 - 730806754528*T^2 - 480596018176624*T - 6505338019626848
$97$
\( T^{6} - 1584 T^{5} + \cdots - 13\!\cdots\!16 \)
T^6 - 1584*T^5 - 1969640*T^4 + 3033553624*T^3 + 499162106428*T^2 - 610881653965600*T - 131573697903949616
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