[N,k,chi] = [260,4,Mod(1,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("260.1");
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
\(2\)
\(-1\)
\(5\)
\(1\)
\(13\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{4} - 4T_{3}^{3} - 64T_{3}^{2} + 40T_{3} + 228 \)
T3^4 - 4*T3^3 - 64*T3^2 + 40*T3 + 228
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(260))\).
$p$
$F_p(T)$
$2$
\( T^{4} \)
T^4
$3$
\( T^{4} - 4 T^{3} - 64 T^{2} + 40 T + 228 \)
T^4 - 4*T^3 - 64*T^2 + 40*T + 228
$5$
\( (T + 5)^{4} \)
(T + 5)^4
$7$
\( T^{4} + 8 T^{3} - 824 T^{2} + \cdots + 7632 \)
T^4 + 8*T^3 - 824*T^2 - 2592*T + 7632
$11$
\( T^{4} - 28 T^{3} - 3864 T^{2} + \cdots + 2100852 \)
T^4 - 28*T^3 - 3864*T^2 + 65928*T + 2100852
$13$
\( (T - 13)^{4} \)
(T - 13)^4
$17$
\( T^{4} - 200 T^{3} + \cdots - 14951088 \)
T^4 - 200*T^3 + 600*T^2 + 1218912*T - 14951088
$19$
\( T^{4} - 132 T^{3} - 4136 T^{2} + \cdots - 8535020 \)
T^4 - 132*T^3 - 4136*T^2 + 813336*T - 8535020
$23$
\( T^{4} - 244 T^{3} + \cdots + 29171364 \)
T^4 - 244*T^3 + 496*T^2 + 1669320*T + 29171364
$29$
\( T^{4} + 8 T^{3} - 44448 T^{2} + \cdots + 293007168 \)
T^4 + 8*T^3 - 44448*T^2 - 1330368*T + 293007168
$31$
\( T^{4} - 292 T^{3} + \cdots - 642276076 \)
T^4 - 292*T^3 - 31224*T^2 + 11461048*T - 642276076
$37$
\( T^{4} - 168 T^{3} + \cdots + 805400832 \)
T^4 - 168*T^3 - 83424*T^2 + 12052096*T + 805400832
$41$
\( T^{4} - 280 T^{3} + \cdots + 496536912 \)
T^4 - 280*T^3 - 76200*T^2 + 1118496*T + 496536912
$43$
\( T^{4} - 452 T^{3} + \cdots - 45746748 \)
T^4 - 452*T^3 - 80560*T^2 + 14750792*T - 45746748
$47$
\( T^{4} + 280 T^{3} + \cdots + 1647798480 \)
T^4 + 280*T^3 - 156792*T^2 - 3192672*T + 1647798480
$53$
\( T^{4} - 584 T^{3} + \cdots - 168468912 \)
T^4 - 584*T^3 - 102504*T^2 + 11222880*T - 168468912
$59$
\( T^{4} + 708 T^{3} + \cdots + 777261396 \)
T^4 + 708*T^3 + 51896*T^2 - 26767896*T + 777261396
$61$
\( T^{4} - 1128 T^{3} + \cdots - 21509627072 \)
T^4 - 1128*T^3 + 184480*T^2 + 91760832*T - 21509627072
$67$
\( T^{4} - 176 T^{3} + \cdots + 33912154512 \)
T^4 - 176*T^3 - 403096*T^2 + 35564096*T + 33912154512
$71$
\( T^{4} + 1028 T^{3} + \cdots - 3387108492 \)
T^4 + 1028*T^3 + 10776*T^2 - 77360856*T - 3387108492
$73$
\( T^{4} - 664 T^{3} + \cdots + 67723906304 \)
T^4 - 664*T^3 - 1000992*T^2 + 529164160*T + 67723906304
$79$
\( T^{4} + 728 T^{3} + \cdots + 245418881600 \)
T^4 + 728*T^3 - 1132416*T^2 - 426310592*T + 245418881600
$83$
\( T^{4} - 552 T^{3} + \cdots - 311448240 \)
T^4 - 552*T^3 - 369048*T^2 - 41350752*T - 311448240
$89$
\( T^{4} + 2824 T^{3} + \cdots + 46519298064 \)
T^4 + 2824*T^3 + 1494808*T^2 - 712045536*T + 46519298064
$97$
\( T^{4} - 1160 T^{3} + \cdots - 226545046512 \)
T^4 - 1160*T^3 - 471784*T^2 + 871399904*T - 226545046512
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