[N,k,chi] = [26,6,Mod(1,26)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(26, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("26.1");
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 \(\beta = \frac{1}{2}(1 + \sqrt{849})\).
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
\(2\)
\(-1\)
\(13\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} - 9T_{3} - 192 \)
T3^2 - 9*T3 - 192
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(26))\).
$p$
$F_p(T)$
$2$
\( (T - 4)^{2} \)
(T - 4)^2
$3$
\( T^{2} - 9T - 192 \)
T^2 - 9*T - 192
$5$
\( T^{2} - 73T - 578 \)
T^2 - 73*T - 578
$7$
\( T^{2} - 155T - 11186 \)
T^2 - 155*T - 11186
$11$
\( T^{2} + 220T - 110156 \)
T^2 + 220*T - 110156
$13$
\( (T + 169)^{2} \)
(T + 169)^2
$17$
\( T^{2} + 189 T - 3523122 \)
T^2 + 189*T - 3523122
$19$
\( T^{2} + 2496 T + 793404 \)
T^2 + 2496*T + 793404
$23$
\( T^{2} + 3044 T - 159200 \)
T^2 + 3044*T - 159200
$29$
\( T^{2} - 1900 T - 13890476 \)
T^2 - 1900*T - 13890476
$31$
\( T^{2} - 2798 T - 28369928 \)
T^2 - 2798*T - 28369928
$37$
\( T^{2} - 17805 T + 72604926 \)
T^2 - 17805*T + 72604926
$41$
\( T^{2} - 11634 T - 11466000 \)
T^2 - 11634*T - 11466000
$43$
\( T^{2} + 4069 T - 6040532 \)
T^2 + 4069*T - 6040532
$47$
\( T^{2} + 25489 T + 127607974 \)
T^2 + 25489*T + 127607974
$53$
\( T^{2} + 4614 T - 129839400 \)
T^2 + 4614*T - 129839400
$59$
\( T^{2} + 23420 T + 92989684 \)
T^2 + 23420*T + 92989684
$61$
\( T^{2} - 96830 T + 2309711776 \)
T^2 - 96830*T + 2309711776
$67$
\( T^{2} - 72440 T + 1295720044 \)
T^2 - 72440*T + 1295720044
$71$
\( T^{2} + 36679 T - 1862988962 \)
T^2 + 36679*T - 1862988962
$73$
\( T^{2} - 47152 T - 1462893860 \)
T^2 - 47152*T - 1462893860
$79$
\( T^{2} - 52024 T + 439936528 \)
T^2 - 52024*T + 439936528
$83$
\( T^{2} + 37758 T + 83472480 \)
T^2 + 37758*T + 83472480
$89$
\( T^{2} + 105072 T + 1072134396 \)
T^2 + 105072*T + 1072134396
$97$
\( T^{2} - 104392 T - 4229773940 \)
T^2 - 104392*T - 4229773940
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