[N,k,chi] = [784,6,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("784.1");
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 \(\beta = \sqrt{37}\).
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
\(2\)
\(-1\)
\(7\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} + 8T_{3} - 21 \)
T3^2 + 8*T3 - 21
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(784))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} + 8T - 21 \)
T^2 + 8*T - 21
$5$
\( T^{2} - 38T - 3339 \)
T^2 - 38*T - 3339
$7$
\( T^{2} \)
T^2
$11$
\( T^{2} + 424T + 25371 \)
T^2 + 424*T + 25371
$13$
\( T^{2} - 924T + 184436 \)
T^2 - 924*T + 184436
$17$
\( T^{2} - 2346 T + 731241 \)
T^2 - 2346*T + 731241
$19$
\( T^{2} + 360 T - 2806573 \)
T^2 + 360*T - 2806573
$23$
\( T^{2} - 12T - 176121 \)
T^2 - 12*T - 176121
$29$
\( T^{2} + 7052 T - 5697324 \)
T^2 + 7052*T - 5697324
$31$
\( T^{2} - 3548 T - 15768249 \)
T^2 - 3548*T - 15768249
$37$
\( T^{2} - 11090 T + 7655325 \)
T^2 - 11090*T + 7655325
$41$
\( T^{2} + 3500 T - 24814188 \)
T^2 + 3500*T - 24814188
$43$
\( T^{2} - 12680 T - 26638832 \)
T^2 - 12680*T - 26638832
$47$
\( T^{2} + 22956 T + 32835159 \)
T^2 + 22956*T + 32835159
$53$
\( T^{2} - 3042 T - 119976147 \)
T^2 - 3042*T - 119976147
$59$
\( T^{2} + 65808 T + 1072240659 \)
T^2 + 65808*T + 1072240659
$61$
\( T^{2} - 42486 T - 187196443 \)
T^2 - 42486*T - 187196443
$67$
\( T^{2} + 42312 T + 416327579 \)
T^2 + 42312*T + 416327579
$71$
\( T^{2} - 2208 T - 175265856 \)
T^2 - 2208*T - 175265856
$73$
\( T^{2} - 50506 T - 1373102199 \)
T^2 - 50506*T - 1373102199
$79$
\( T^{2} + 9004 T - 977520209 \)
T^2 + 9004*T - 977520209
$83$
\( T^{2} + 104328 T + 1959796944 \)
T^2 + 104328*T + 1959796944
$89$
\( T^{2} - 26666 T - 3061016343 \)
T^2 - 26666*T - 3061016343
$97$
\( T^{2} + 209132 T + 10932626964 \)
T^2 + 209132*T + 10932626964
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