[N,k,chi] = [59,4,Mod(1,59)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(59, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("59.1");
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 \(\beta = \frac{1}{2}(1 + \sqrt{17})\).
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
\(59\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{2} - T_{2} - 4 \)
T2^2 - T2 - 4
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(59))\).
$p$
$F_p(T)$
$2$
\( T^{2} - T - 4 \)
T^2 - T - 4
$3$
\( T^{2} + T - 38 \)
T^2 + T - 38
$5$
\( T^{2} + 31T + 202 \)
T^2 + 31*T + 202
$7$
\( T^{2} + 8T - 1 \)
T^2 + 8*T - 1
$11$
\( T^{2} - 13T + 38 \)
T^2 - 13*T + 38
$13$
\( T^{2} + 95T + 1912 \)
T^2 + 95*T + 1912
$17$
\( T^{2} - 169T + 7102 \)
T^2 - 169*T + 7102
$19$
\( T^{2} + 107T - 236 \)
T^2 + 107*T - 236
$23$
\( T^{2} + 96T - 144 \)
T^2 + 96*T - 144
$29$
\( T^{2} + 307T + 7748 \)
T^2 + 307*T + 7748
$31$
\( T^{2} - 56T - 9008 \)
T^2 - 56*T - 9008
$37$
\( T^{2} + 291T + 9232 \)
T^2 + 291*T + 9232
$41$
\( T^{2} - 452T + 36779 \)
T^2 - 452*T + 36779
$43$
\( T^{2} + 35T - 11632 \)
T^2 + 35*T - 11632
$47$
\( T^{2} - 26T - 47584 \)
T^2 - 26*T - 47584
$53$
\( T^{2} + 641T + 5816 \)
T^2 + 641*T + 5816
$59$
\( (T - 59)^{2} \)
(T - 59)^2
$61$
\( T^{2} + 604T + 30004 \)
T^2 + 604*T + 30004
$67$
\( T^{2} + 1326 T + 322456 \)
T^2 + 1326*T + 322456
$71$
\( T^{2} - 289T - 805664 \)
T^2 - 289*T - 805664
$73$
\( T^{2} - 48T - 252452 \)
T^2 - 48*T - 252452
$79$
\( T^{2} + 224T + 9671 \)
T^2 + 224*T + 9671
$83$
\( T^{2} - 1963 T + 939436 \)
T^2 - 1963*T + 939436
$89$
\( T^{2} - 688T - 420292 \)
T^2 - 688*T - 420292
$97$
\( T^{2} - 356 T - 1887548 \)
T^2 - 356*T - 1887548
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