[N,k,chi] = [560,6,Mod(1,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, 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("560.1");
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
sage: f.q_expansion() # note that sage often uses an isomorphic number field
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{65})\).
We also show the integral \(q\)-expansion of the trace form .
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
\( T_{3}^{2} + 3T_{3} - 144 \)
T3^2 + 3*T3 - 144
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(560))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} + 3T - 144 \)
T^2 + 3*T - 144
$5$
\( (T + 25)^{2} \)
(T + 25)^2
$7$
\( (T - 49)^{2} \)
(T - 49)^2
$11$
\( T^{2} - 601T - 62596 \)
T^2 - 601*T - 62596
$13$
\( T^{2} + 577T + 37586 \)
T^2 + 577*T + 37586
$17$
\( T^{2} - 41T - 1023346 \)
T^2 - 41*T - 1023346
$19$
\( T^{2} + 630T - 20960 \)
T^2 + 630*T - 20960
$23$
\( T^{2} - 442 T - 13172224 \)
T^2 - 442*T - 13172224
$29$
\( T^{2} - 5885 T - 5853350 \)
T^2 - 5885*T - 5853350
$31$
\( T^{2} - 396 T - 13834656 \)
T^2 - 396*T - 13834656
$37$
\( T^{2} + 8904 T - 5978196 \)
T^2 + 8904*T - 5978196
$41$
\( T^{2} - 1774 T - 236091496 \)
T^2 - 1774*T - 236091496
$43$
\( T^{2} - 27122 T + 170086856 \)
T^2 - 27122*T + 170086856
$47$
\( T^{2} - 21289 T + 72995224 \)
T^2 - 21289*T + 72995224
$53$
\( T^{2} + 55582 T + 768990296 \)
T^2 + 55582*T + 768990296
$59$
\( T^{2} + 59600 T + 451339840 \)
T^2 + 59600*T + 451339840
$61$
\( T^{2} + 51846 T + 142927344 \)
T^2 + 51846*T + 142927344
$67$
\( T^{2} - 45344 T + 174936944 \)
T^2 - 45344*T + 174936944
$71$
\( T^{2} + 80744 T + 1172746624 \)
T^2 + 80744*T + 1172746624
$73$
\( T^{2} + 13532 T - 239780284 \)
T^2 + 13532*T - 239780284
$79$
\( T^{2} - 51795 T - 4382959400 \)
T^2 - 51795*T - 4382959400
$83$
\( T^{2} + 109828 T + 2765333536 \)
T^2 + 109828*T + 2765333536
$89$
\( T^{2} + 37650 T - 177665240 \)
T^2 + 37650*T - 177665240
$97$
\( T^{2} + 96339 T - 838817066 \)
T^2 + 96339*T - 838817066
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