[N,k,chi] = [280,6,Mod(1,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, 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("280.1");
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
\(2\)
\(1\)
\(5\)
\(1\)
\(7\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{3} - 14T_{3}^{2} - 267T_{3} + 1800 \)
T3^3 - 14*T3^2 - 267*T3 + 1800
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(280))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( T^{3} - 14 T^{2} - 267 T + 1800 \)
T^3 - 14*T^2 - 267*T + 1800
$5$
\( (T + 25)^{3} \)
(T + 25)^3
$7$
\( (T - 49)^{3} \)
(T - 49)^3
$11$
\( T^{3} + 50 T^{2} - 201871 T - 32091540 \)
T^3 + 50*T^2 - 201871*T - 32091540
$13$
\( T^{3} - 536 T^{2} + \cdots + 40540670 \)
T^3 - 536*T^2 - 48247*T + 40540670
$17$
\( T^{3} - 268 T^{2} + \cdots - 1677666906 \)
T^3 - 268*T^2 - 3291415*T - 1677666906
$19$
\( T^{3} + 1048 T^{2} + \cdots - 339889184 \)
T^3 + 1048*T^2 - 1505300*T - 339889184
$23$
\( T^{3} + 576 T^{2} + \cdots - 470543360 \)
T^3 + 576*T^2 - 1352276*T - 470543360
$29$
\( T^{3} - 6172 T^{2} + \cdots - 4080790758 \)
T^3 - 6172*T^2 + 10463789*T - 4080790758
$31$
\( T^{3} + 2404 T^{2} + \cdots - 42412572288 \)
T^3 + 2404*T^2 - 17610160*T - 42412572288
$37$
\( T^{3} - 7806 T^{2} + \cdots + 754109894424 \)
T^3 - 7806*T^2 - 149807924*T + 754109894424
$41$
\( T^{3} - 12150 T^{2} + \cdots + 859615169760 \)
T^3 - 12150*T^2 - 119300744*T + 859615169760
$43$
\( T^{3} - 16868 T^{2} + \cdots + 770989825360 \)
T^3 - 16868*T^2 - 103118228*T + 770989825360
$47$
\( T^{3} - 30230 T^{2} + \cdots - 822133181192 \)
T^3 - 30230*T^2 + 284100877*T - 822133181192
$53$
\( T^{3} - 25862 T^{2} + \cdots - 640341284960 \)
T^3 - 25862*T^2 + 222911296*T - 640341284960
$59$
\( T^{3} - 36352 T^{2} + \cdots + 2921311866880 \)
T^3 - 36352*T^2 - 565179904*T + 2921311866880
$61$
\( T^{3} - 6534 T^{2} + \cdots - 5471960282336 \)
T^3 - 6534*T^2 - 980556296*T - 5471960282336
$67$
\( T^{3} - 45708 T^{2} + \cdots + 17305695495360 \)
T^3 - 45708*T^2 - 1079349008*T + 17305695495360
$71$
\( T^{3} - 57456 T^{2} + \cdots + 5500862115840 \)
T^3 - 57456*T^2 + 13886208*T + 5500862115840
$73$
\( T^{3} + 17346 T^{2} + \cdots - 2212406609000 \)
T^3 + 17346*T^2 - 438116180*T - 2212406609000
$79$
\( T^{3} - 21222 T^{2} + \cdots - 14445274057688 \)
T^3 - 21222*T^2 - 2282948031*T - 14445274057688
$83$
\( T^{3} + \cdots + 193963320099072 \)
T^3 - 128816*T^2 + 224524080*T + 193963320099072
$89$
\( T^{3} + \cdots + 107630146696800 \)
T^3 - 132286*T^2 + 708035288*T + 107630146696800
$97$
\( T^{3} + \cdots - 147037236625098 \)
T^3 + 74348*T^2 - 1589692911*T - 147037236625098
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