[N,k,chi] = [912,6,Mod(1,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("912.1");
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
\(2\)
\(-1\)
\(3\)
\(1\)
\(19\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{3} + 5T_{5}^{2} - 2158T_{5} - 37112 \)
T5^3 + 5*T5^2 - 2158*T5 - 37112
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(912))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( (T + 9)^{3} \)
(T + 9)^3
$5$
\( T^{3} + 5 T^{2} - 2158 T - 37112 \)
T^3 + 5*T^2 - 2158*T - 37112
$7$
\( T^{3} - 33 T^{2} - 23412 T + 1656000 \)
T^3 - 33*T^2 - 23412*T + 1656000
$11$
\( T^{3} - 695 T^{2} + \cdots + 26278976 \)
T^3 - 695*T^2 + 36884*T + 26278976
$13$
\( T^{3} + 996 T^{2} + \cdots - 178271216 \)
T^3 + 996*T^2 - 176628*T - 178271216
$17$
\( T^{3} + 765 T^{2} + \cdots - 426321684 \)
T^3 + 765*T^2 - 788292*T - 426321684
$19$
\( (T - 361)^{3} \)
(T - 361)^3
$23$
\( T^{3} - 1202 T^{2} + \cdots - 209746912 \)
T^3 - 1202*T^2 - 5948944*T - 209746912
$29$
\( T^{3} + 5518 T^{2} + \cdots + 10400234888 \)
T^3 + 5518*T^2 - 25587940*T + 10400234888
$31$
\( T^{3} - 5760 T^{2} + \cdots + 309849129472 \)
T^3 - 5760*T^2 - 54881988*T + 309849129472
$37$
\( T^{3} + 11118 T^{2} + \cdots - 969802262848 \)
T^3 + 11118*T^2 - 87271752*T - 969802262848
$41$
\( T^{3} + 6592 T^{2} + \cdots - 220780939552 \)
T^3 + 6592*T^2 - 39147412*T - 220780939552
$43$
\( T^{3} - 5889 T^{2} + \cdots + 2706921550192 \)
T^3 - 5889*T^2 - 300071016*T + 2706921550192
$47$
\( T^{3} - 6311 T^{2} + \cdots + 484607665592 \)
T^3 - 6311*T^2 - 87753070*T + 484607665592
$53$
\( T^{3} - 9286 T^{2} + \cdots + 17693656641400 \)
T^3 - 9286*T^2 - 1116995380*T + 17693656641400
$59$
\( T^{3} - 39624 T^{2} + \cdots + 12187656460800 \)
T^3 - 39624*T^2 - 485320368*T + 12187656460800
$61$
\( T^{3} + 42693 T^{2} + \cdots - 10787695490636 \)
T^3 + 42693*T^2 + 13638048*T - 10787695490636
$67$
\( T^{3} - 75060 T^{2} + \cdots + 8518946717952 \)
T^3 - 75060*T^2 + 258349632*T + 8518946717952
$71$
\( T^{3} - 77828 T^{2} + \cdots + 8724141842432 \)
T^3 - 77828*T^2 + 1005151808*T + 8724141842432
$73$
\( T^{3} + 66867 T^{2} + \cdots + 7419579873444 \)
T^3 + 66867*T^2 + 1280203188*T + 7419579873444
$79$
\( T^{3} - 82950 T^{2} + \cdots + 4752096482816 \)
T^3 - 82950*T^2 + 1572659088*T + 4752096482816
$83$
\( T^{3} - 69372 T^{2} + \cdots + 89984667239424 \)
T^3 - 69372*T^2 - 928485504*T + 89984667239424
$89$
\( T^{3} - 138726 T^{2} + \cdots + 14\!\cdots\!80 \)
T^3 - 138726*T^2 - 10515658404*T + 1449227357461080
$97$
\( T^{3} + 90186 T^{2} + \cdots - 15\!\cdots\!68 \)
T^3 + 90186*T^2 - 17635135716*T - 1559430545896168
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