[N,k,chi] = [490,6,Mod(1,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("490.1");
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 \(\beta = 2\sqrt{79}\).
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
\( T_{3}^{2} - 6T_{3} - 307 \)
T3^2 - 6*T3 - 307
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(490))\).
$p$
$F_p(T)$
$2$
\( (T + 4)^{2} \)
(T + 4)^2
$3$
\( T^{2} - 6T - 307 \)
T^2 - 6*T - 307
$5$
\( (T + 25)^{2} \)
(T + 25)^2
$7$
\( T^{2} \)
T^2
$11$
\( T^{2} + 76T + 180 \)
T^2 + 76*T + 180
$13$
\( T^{2} - 732T - 18988 \)
T^2 - 732*T - 18988
$17$
\( T^{2} + 3012 T + 2256660 \)
T^2 + 3012*T + 2256660
$19$
\( T^{2} - 1160 T - 1788384 \)
T^2 - 1160*T - 1788384
$23$
\( T^{2} + 3518 T + 2206437 \)
T^2 + 3518*T + 2206437
$29$
\( T^{2} - 3286 T + 1405113 \)
T^2 - 3286*T + 1405113
$31$
\( T^{2} - 18228 T + 82984100 \)
T^2 - 18228*T + 82984100
$37$
\( T^{2} - 2896 T - 44499392 \)
T^2 - 2896*T - 44499392
$41$
\( T^{2} + 26174 T + 140113233 \)
T^2 + 26174*T + 140113233
$43$
\( T^{2} + 13298 T - 55242635 \)
T^2 + 13298*T - 55242635
$47$
\( T^{2} + 16472 T - 196153440 \)
T^2 + 16472*T - 196153440
$53$
\( T^{2} + 14960 T + 52399824 \)
T^2 + 14960*T + 52399824
$59$
\( T^{2} - 37816 T + 57730848 \)
T^2 - 37816*T + 57730848
$61$
\( T^{2} + 3274 T - 1784263575 \)
T^2 + 3274*T - 1784263575
$67$
\( T^{2} - 41438 T + 428973285 \)
T^2 - 41438*T + 428973285
$71$
\( T^{2} - 8520 T - 314498016 \)
T^2 - 8520*T - 314498016
$73$
\( T^{2} - 28676 T - 4032058860 \)
T^2 - 28676*T - 4032058860
$79$
\( T^{2} - 3552 T - 80331760 \)
T^2 - 3552*T - 80331760
$83$
\( T^{2} + 54982 T + 639325197 \)
T^2 + 54982*T + 639325197
$89$
\( T^{2} - 81578 T - 531982215 \)
T^2 - 81578*T - 531982215
$97$
\( T^{2} + 106964 T + 737289700 \)
T^2 + 106964*T + 737289700
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