[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
sage: f.q_expansion() # note that sage often uses an isomorphic number field
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 2\sqrt{109}\).
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
\( T_{3}^{2} - 2T_{3} - 435 \)
T3^2 - 2*T3 - 435
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(280))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} - 2T - 435 \)
T^2 - 2*T - 435
$5$
\( (T - 25)^{2} \)
(T - 25)^2
$7$
\( (T + 49)^{2} \)
(T + 49)^2
$11$
\( T^{2} + 254T - 125135 \)
T^2 + 254*T - 125135
$13$
\( T^{2} + 1342 T + 414925 \)
T^2 + 1342*T + 414925
$17$
\( T^{2} + 1786 T + 430773 \)
T^2 + 1786*T + 430773
$19$
\( T^{2} - 1976 T + 442044 \)
T^2 - 1976*T + 442044
$23$
\( T^{2} + 2112 T - 7552980 \)
T^2 + 2112*T - 7552980
$29$
\( T^{2} + 4762 T + 1978857 \)
T^2 + 4762*T + 1978857
$31$
\( T^{2} - 13692 T + 46392912 \)
T^2 - 13692*T + 46392912
$37$
\( T^{2} - 2136 T - 62149572 \)
T^2 - 2136*T - 62149572
$41$
\( T^{2} + 6740 T - 4883664 \)
T^2 + 6740*T - 4883664
$43$
\( T^{2} + 26728 T + 174494172 \)
T^2 + 26728*T + 174494172
$47$
\( T^{2} + 6326 T - 117604347 \)
T^2 + 6326*T - 117604347
$53$
\( T^{2} - 24624 T - 31492800 \)
T^2 - 24624*T - 31492800
$59$
\( T^{2} - 51336 T + 84240080 \)
T^2 - 51336*T + 84240080
$61$
\( T^{2} - 4468 T - 517784144 \)
T^2 - 4468*T - 517784144
$67$
\( T^{2} + 39168 T - 235963648 \)
T^2 + 39168*T - 235963648
$71$
\( T^{2} - 41232 T - 2308707520 \)
T^2 - 41232*T - 2308707520
$73$
\( T^{2} + 36124 T - 1857532940 \)
T^2 + 36124*T - 1857532940
$79$
\( T^{2} + 140842 T + 4901982057 \)
T^2 + 140842*T + 4901982057
$83$
\( T^{2} + 57712 T - 1390305168 \)
T^2 + 57712*T - 1390305168
$89$
\( T^{2} + 20236 T - 37795280 \)
T^2 + 20236*T - 37795280
$97$
\( T^{2} + 183586 T + 4634236813 \)
T^2 + 183586*T + 4634236813
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