[N,k,chi] = [722,6,Mod(1,722)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(722, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("722.1");
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
\(2\)
\(1\)
\(19\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{4} - T_{3}^{3} - 924T_{3}^{2} + 3360T_{3} + 110592 \)
T3^4 - T3^3 - 924*T3^2 + 3360*T3 + 110592
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(722))\).
$p$
$F_p(T)$
$2$
\( (T + 4)^{4} \)
(T + 4)^4
$3$
\( T^{4} - T^{3} - 924 T^{2} + \cdots + 110592 \)
T^4 - T^3 - 924*T^2 + 3360*T + 110592
$5$
\( T^{4} + 14 T^{3} - 5943 T^{2} + \cdots + 3840812 \)
T^4 + 14*T^3 - 5943*T^2 - 117944*T + 3840812
$7$
\( T^{4} - 97 T^{3} - 53541 T^{2} + \cdots - 91211508 \)
T^4 - 97*T^3 - 53541*T^2 + 7070841*T - 91211508
$11$
\( T^{4} - 758 T^{3} + \cdots - 6028722256 \)
T^4 - 758*T^3 - 93585*T^2 + 125154062*T - 6028722256
$13$
\( T^{4} + 1465 T^{3} + \cdots - 55296000 \)
T^4 + 1465*T^3 + 604464*T^2 + 55563264*T - 55296000
$17$
\( T^{4} - 599 T^{3} + \cdots - 1007551906110 \)
T^4 - 599*T^3 - 2799763*T^2 + 3355000487*T - 1007551906110
$19$
\( T^{4} \)
T^4
$23$
\( T^{4} + 3651 T^{3} + \cdots - 2602166692160 \)
T^4 + 3651*T^3 - 2188268*T^2 - 6969989616*T - 2602166692160
$29$
\( T^{4} - 12451 T^{3} + \cdots - 63244006861824 \)
T^4 - 12451*T^3 + 38121372*T^2 + 5123961504*T - 63244006861824
$31$
\( T^{4} + 3038 T^{3} + \cdots + 47054539063296 \)
T^4 + 3038*T^3 - 84099000*T^2 - 132849665856*T + 47054539063296
$37$
\( T^{4} + \cdots - 187250082600960 \)
T^4 + 10282*T^3 - 68861352*T^2 - 276935916096*T - 187250082600960
$41$
\( T^{4} + 6520 T^{3} + \cdots - 33\!\cdots\!00 \)
T^4 + 6520*T^3 - 273948048*T^2 - 1959148536192*T - 3301343098675200
$43$
\( T^{4} + \cdots - 994614017440000 \)
T^4 + 2330*T^3 - 98295633*T^2 - 624962063450*T - 994614017440000
$47$
\( T^{4} - 12760 T^{3} + \cdots + 40\!\cdots\!00 \)
T^4 - 12760*T^3 - 673694725*T^2 + 8519672877892*T + 40157092579296000
$53$
\( T^{4} + 78509 T^{3} + \cdots + 12\!\cdots\!44 \)
T^4 + 78509*T^3 + 1796883588*T^2 + 10246627048608*T + 12935477277471744
$59$
\( T^{4} - 20605 T^{3} + \cdots + 58\!\cdots\!92 \)
T^4 - 20605*T^3 - 1924252632*T^2 + 4704370565760*T + 580980108899745792
$61$
\( T^{4} - 36040 T^{3} + \cdots + 35\!\cdots\!40 \)
T^4 - 36040*T^3 - 2080269855*T^2 + 64667568977802*T + 359879784102627840
$67$
\( T^{4} + 42707 T^{3} + \cdots - 54\!\cdots\!20 \)
T^4 + 42707*T^3 + 151812516*T^2 - 9417329580384*T - 54201788365086720
$71$
\( T^{4} - 24000 T^{3} + \cdots - 66\!\cdots\!20 \)
T^4 - 24000*T^3 - 2257834176*T^2 + 63892555232256*T - 6615620977950720
$73$
\( T^{4} + 55595 T^{3} + \cdots - 18\!\cdots\!38 \)
T^4 + 55595*T^3 - 520307643*T^2 - 44179926161215*T - 18330794705066738
$79$
\( T^{4} + 81936 T^{3} + \cdots - 11\!\cdots\!76 \)
T^4 + 81936*T^3 - 2397748464*T^2 - 130816158717312*T - 1185132344742936576
$83$
\( T^{4} + 173966 T^{3} + \cdots - 52\!\cdots\!16 \)
T^4 + 173966*T^3 + 6643930944*T^2 - 9398154947072*T - 520595724422742016
$89$
\( T^{4} + 35682 T^{3} + \cdots + 53\!\cdots\!36 \)
T^4 + 35682*T^3 - 16108652952*T^2 - 181714797652032*T + 53927672338456436736
$97$
\( T^{4} + 44748 T^{3} + \cdots - 10\!\cdots\!92 \)
T^4 + 44748*T^3 - 17447903136*T^2 - 1232222471880192*T - 10305393974169403392
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