[N,k,chi] = [100,6,Mod(1,100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(100, 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("100.1");
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 \(\beta = \sqrt{409}\).
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
\(2\)
\(-1\)
\(5\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} + 20T_{3} - 309 \)
T3^2 + 20*T3 - 309
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(100))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} + 20T - 309 \)
T^2 + 20*T - 309
$5$
\( T^{2} \)
T^2
$7$
\( T^{2} - 40T - 14324 \)
T^2 - 40*T - 14324
$11$
\( T^{2} + 60T - 91125 \)
T^2 + 60*T - 91125
$13$
\( T^{2} + 920T - 23984 \)
T^2 + 920*T - 23984
$17$
\( T^{2} + 2910 T + 2058129 \)
T^2 + 2910*T + 2058129
$19$
\( T^{2} - 2092 T + 265891 \)
T^2 - 2092*T + 265891
$23$
\( T^{2} + 120 T - 7785396 \)
T^2 + 120*T - 7785396
$29$
\( T^{2} - 3552 T - 20404224 \)
T^2 - 3552*T - 20404224
$31$
\( T^{2} + 8888 T + 10546636 \)
T^2 + 8888*T + 10546636
$37$
\( T^{2} + 12140 T - 48200924 \)
T^2 + 12140*T - 48200924
$41$
\( T^{2} + 12438 T - 14330439 \)
T^2 + 12438*T - 14330439
$43$
\( T^{2} + 1160 T - 23222000 \)
T^2 + 1160*T - 23222000
$47$
\( T^{2} - 1200 T - 6766416 \)
T^2 - 1200*T - 6766416
$53$
\( T^{2} + 26340 T + 105365124 \)
T^2 + 26340*T + 105365124
$59$
\( T^{2} + 36696 T - 194887296 \)
T^2 + 36696*T - 194887296
$61$
\( T^{2} - 19204 T - 1062163196 \)
T^2 - 19204*T - 1062163196
$67$
\( T^{2} - 90460 T + 1878749611 \)
T^2 - 90460*T + 1878749611
$71$
\( T^{2} - 2736 T - 1601572176 \)
T^2 - 2736*T - 1601572176
$73$
\( T^{2} + 12770 T + 37882321 \)
T^2 + 12770*T + 37882321
$79$
\( T^{2} + 16184 T + 3271564 \)
T^2 + 16184*T + 3271564
$83$
\( T^{2} - 30300 T - 3821053581 \)
T^2 - 30300*T - 3821053581
$89$
\( T^{2} + 47322 T - 12174944679 \)
T^2 + 47322*T - 12174944679
$97$
\( T^{2} - 2980 T - 3059429564 \)
T^2 - 2980*T - 3059429564
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