[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 \(\beta = \sqrt{193}\).
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
\( T_{3}^{2} + 14T_{3} - 144 \)
T3^2 + 14*T3 - 144
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(784))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} + 14T - 144 \)
T^2 + 14*T - 144
$5$
\( T^{2} + 42T - 4384 \)
T^2 + 42*T - 4384
$7$
\( T^{2} \)
T^2
$11$
\( T^{2} - 716T + 90336 \)
T^2 - 716*T + 90336
$13$
\( T^{2} - 714T + 71672 \)
T^2 - 714*T + 71672
$17$
\( T^{2} - 1344 T - 111204 \)
T^2 - 1344*T - 111204
$19$
\( T^{2} + 1946 T - 722528 \)
T^2 + 1946*T - 722528
$23$
\( T^{2} - 1792 T - 1618176 \)
T^2 - 1792*T - 1618176
$29$
\( T^{2} + 1200 T - 57176388 \)
T^2 + 1200*T - 57176388
$31$
\( T^{2} + 6804 T - 26817184 \)
T^2 + 6804*T - 26817184
$37$
\( T^{2} - 14640 T + 49005212 \)
T^2 - 14640*T + 49005212
$41$
\( T^{2} + 7896 T - 22118548 \)
T^2 + 7896*T - 22118548
$43$
\( T^{2} + 524 T - 51717888 \)
T^2 + 524*T - 51717888
$47$
\( T^{2} + 18396 T - 22804384 \)
T^2 + 18396*T - 22804384
$53$
\( T^{2} - 45132 T + 313124004 \)
T^2 - 45132*T + 313124004
$59$
\( T^{2} - 22582 T + 101774256 \)
T^2 - 22582*T + 101774256
$61$
\( T^{2} - 52822 T + 456736944 \)
T^2 - 52822*T + 456736944
$67$
\( T^{2} + 9848 T + 14561808 \)
T^2 + 9848*T + 14561808
$71$
\( T^{2} - 840 T - 3181158400 \)
T^2 - 840*T - 3181158400
$73$
\( T^{2} - 122052 T + 3444396788 \)
T^2 - 122052*T + 3444396788
$79$
\( T^{2} + 31704 T - 112014208 \)
T^2 + 31704*T - 112014208
$83$
\( T^{2} - 36974 T - 3038476256 \)
T^2 - 36974*T - 3038476256
$89$
\( T^{2} - 210588 T + 10645600644 \)
T^2 - 210588*T + 10645600644
$97$
\( T^{2} - 44240 T - 14736460932 \)
T^2 - 44240*T - 14736460932
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