[N,k,chi] = [1560,4,Mod(1,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 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("1560.1");
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
\(2\)
\(-1\)
\(3\)
\(1\)
\(5\)
\(-1\)
\(13\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{7}^{6} + 18T_{7}^{5} - 1427T_{7}^{4} - 19340T_{7}^{3} + 507356T_{7}^{2} + 2663200T_{7} - 48965280 \)
T7^6 + 18*T7^5 - 1427*T7^4 - 19340*T7^3 + 507356*T7^2 + 2663200*T7 - 48965280
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1560))\).
$p$
$F_p(T)$
$2$
\( T^{6} \)
T^6
$3$
\( (T + 3)^{6} \)
(T + 3)^6
$5$
\( (T - 5)^{6} \)
(T - 5)^6
$7$
\( T^{6} + 18 T^{5} - 1427 T^{4} + \cdots - 48965280 \)
T^6 + 18*T^5 - 1427*T^4 - 19340*T^3 + 507356*T^2 + 2663200*T - 48965280
$11$
\( T^{6} - 7443 T^{4} + \cdots - 7758842112 \)
T^6 - 7443*T^4 - 14806*T^3 + 14691544*T^2 + 6393024*T - 7758842112
$13$
\( (T + 13)^{6} \)
(T + 13)^6
$17$
\( T^{6} - 36 T^{5} + \cdots - 48858044256 \)
T^6 - 36*T^5 - 17847*T^4 + 202018*T^3 + 61011132*T^2 - 132629272*T - 48858044256
$19$
\( T^{6} + 64 T^{5} + \cdots - 9663362176 \)
T^6 + 64*T^5 - 13280*T^4 - 509824*T^3 + 32881424*T^2 + 670629120*T - 9663362176
$23$
\( T^{6} + 28 T^{5} - 41903 T^{4} + \cdots + 91055424 \)
T^6 + 28*T^5 - 41903*T^4 - 684890*T^3 + 219334576*T^2 + 1175016080*T + 91055424
$29$
\( T^{6} - 62 T^{5} + \cdots - 170223974656 \)
T^6 - 62*T^5 - 48896*T^4 - 1191680*T^3 + 298763440*T^2 + 5231415008*T - 170223974656
$31$
\( T^{6} - 214 T^{5} + \cdots - 278767937024 \)
T^6 - 214*T^5 - 63932*T^4 + 20806232*T^3 - 1744680416*T^2 + 42242729088*T - 278767937024
$37$
\( T^{6} - 438 T^{5} + \cdots + 59868044062128 \)
T^6 - 438*T^5 - 74651*T^4 + 45459004*T^3 - 1275919376*T^2 - 808877162384*T + 59868044062128
$41$
\( T^{6} - 342 T^{5} + \cdots + 15167720117616 \)
T^6 - 342*T^5 - 104331*T^4 + 42496028*T^3 - 3101602176*T^2 - 138415045520*T + 15167720117616
$43$
\( T^{6} + \cdots + 252983393722368 \)
T^6 + 64*T^5 - 291856*T^4 + 24909504*T^3 + 22605137920*T^2 - 4888102069248*T + 252983393722368
$47$
\( T^{6} + 690 T^{5} + \cdots + 10\!\cdots\!24 \)
T^6 + 690*T^5 - 246356*T^4 - 212896424*T^3 + 1024003712*T^2 + 13064044973056*T + 1026516877492224
$53$
\( T^{6} + 418 T^{5} + \cdots - 55\!\cdots\!12 \)
T^6 + 418*T^5 - 612087*T^4 - 192741824*T^3 + 109674398568*T^2 + 17193860615136*T - 5500694595788912
$59$
\( T^{6} + 722 T^{5} + \cdots - 39102420828160 \)
T^6 + 722*T^5 - 77448*T^4 - 81295552*T^3 + 6164962048*T^2 + 1054489317376*T - 39102420828160
$61$
\( T^{6} - 658 T^{5} + \cdots - 31\!\cdots\!00 \)
T^6 - 658*T^5 - 693199*T^4 + 330485896*T^3 + 120387317576*T^2 - 31101218413760*T - 3148312073455600
$67$
\( T^{6} + 298 T^{5} + \cdots - 29120342679552 \)
T^6 + 298*T^5 - 825008*T^4 - 304629920*T^3 + 89049430272*T^2 + 22816399154176*T - 29120342679552
$71$
\( T^{6} - 288 T^{5} + \cdots - 19\!\cdots\!16 \)
T^6 - 288*T^5 - 1101115*T^4 + 134055274*T^3 + 304962798816*T^2 - 22276744245824*T - 19274346754594816
$73$
\( T^{6} - 930 T^{5} + \cdots - 10\!\cdots\!28 \)
T^6 - 930*T^5 - 1437856*T^4 + 1372593568*T^3 + 118705700976*T^2 - 110671700700000*T - 10294922541398528
$79$
\( T^{6} + 1594 T^{5} + \cdots - 14\!\cdots\!24 \)
T^6 + 1594*T^5 - 898779*T^4 - 1732413700*T^3 + 183113072960*T^2 + 366447961492864*T - 14791781443073024
$83$
\( T^{6} + 1594 T^{5} + \cdots + 10\!\cdots\!84 \)
T^6 + 1594*T^5 - 2084664*T^4 - 4321790080*T^3 - 38529825024*T^2 + 2626382847319552*T + 1021005223628765184
$89$
\( T^{6} - 1494 T^{5} + \cdots + 94\!\cdots\!60 \)
T^6 - 1494*T^5 - 601027*T^4 + 1483363744*T^3 - 124535091752*T^2 - 358146696187360*T + 94316068249778960
$97$
\( T^{6} - 796 T^{5} + \cdots + 16\!\cdots\!00 \)
T^6 - 796*T^5 - 5323883*T^4 + 4816726650*T^3 + 5969752952276*T^2 - 7342794549271160*T + 1682371851963934400
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