[N,k,chi] = [276,4,Mod(1,276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(276, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("276.1");
S:= CuspForms(chi, 4);
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 \(\beta = \sqrt{13}\).
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
\(2\)
\(-1\)
\(3\)
\(1\)
\(23\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{2} + 2T_{5} - 12 \)
T5^2 + 2*T5 - 12
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(276))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( (T + 3)^{2} \)
(T + 3)^2
$5$
\( T^{2} + 2T - 12 \)
T^2 + 2*T - 12
$7$
\( (T - 2)^{2} \)
(T - 2)^2
$11$
\( T^{2} - 14T - 588 \)
T^2 - 14*T - 588
$13$
\( T^{2} + 24T - 1156 \)
T^2 + 24*T - 1156
$17$
\( T^{2} + 20T - 1200 \)
T^2 + 20*T - 1200
$19$
\( T^{2} + 18T - 15844 \)
T^2 + 18*T - 15844
$23$
\( (T + 23)^{2} \)
(T + 23)^2
$29$
\( T^{2} + 232T + 7164 \)
T^2 + 232*T + 7164
$31$
\( T^{2} + 292T + 2544 \)
T^2 + 292*T + 2544
$37$
\( T^{2} + 410T + 15700 \)
T^2 + 410*T + 15700
$41$
\( T^{2} + 300T + 20628 \)
T^2 + 300*T + 20628
$43$
\( T^{2} + 198T - 67276 \)
T^2 + 198*T - 67276
$47$
\( T^{2} + 120T - 63792 \)
T^2 + 120*T - 63792
$53$
\( T^{2} + 226T - 190356 \)
T^2 + 226*T - 190356
$59$
\( T^{2} - 24T - 269424 \)
T^2 - 24*T - 269424
$61$
\( T^{2} + 462T + 42428 \)
T^2 + 462*T + 42428
$67$
\( T^{2} - 190T + 7972 \)
T^2 - 190*T + 7972
$71$
\( T^{2} - 648T - 643824 \)
T^2 - 648*T - 643824
$73$
\( T^{2} + 640T + 93612 \)
T^2 + 640*T + 93612
$79$
\( T^{2} + 628T - 42012 \)
T^2 + 628*T - 42012
$83$
\( T^{2} - 1730 T + 564132 \)
T^2 - 1730*T + 564132
$89$
\( T^{2} + 72T - 118512 \)
T^2 + 72*T - 118512
$97$
\( T^{2} + 760T - 1668 \)
T^2 + 760*T - 1668
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