[N,k,chi] = [531,4,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("531.1");
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 \(\beta = \sqrt{5}\).
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
\(3\)
\(-1\)
\(59\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{2} - 4T_{2} - 1 \)
T2^2 - 4*T2 - 1
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(531))\).
$p$
$F_p(T)$
$2$
\( T^{2} - 4T - 1 \)
T^2 - 4*T - 1
$3$
\( T^{2} \)
T^2
$5$
\( T^{2} + 6T - 11 \)
T^2 + 6*T - 11
$7$
\( T^{2} + 22T + 101 \)
T^2 + 22*T + 101
$11$
\( T^{2} - 48T + 556 \)
T^2 - 48*T + 556
$13$
\( T^{2} + 32T - 2164 \)
T^2 + 32*T - 2164
$17$
\( T^{2} - 84T - 1116 \)
T^2 - 84*T - 1116
$19$
\( T^{2} + 2T - 1999 \)
T^2 + 2*T - 1999
$23$
\( T^{2} + 164T + 6704 \)
T^2 + 164*T + 6704
$29$
\( T^{2} + 114T - 24131 \)
T^2 + 114*T - 24131
$31$
\( T^{2} + 124T + 3124 \)
T^2 + 124*T + 3124
$37$
\( T^{2} + 292T + 21136 \)
T^2 + 292*T + 21136
$41$
\( T^{2} - 418T + 35681 \)
T^2 - 418*T + 35681
$43$
\( T^{2} + 292T - 4604 \)
T^2 + 292*T - 4604
$47$
\( T^{2} + 48T - 51444 \)
T^2 + 48*T - 51444
$53$
\( T^{2} + 326T + 20789 \)
T^2 + 326*T + 20789
$59$
\( (T + 59)^{2} \)
(T + 59)^2
$61$
\( T^{2} + 268T - 346544 \)
T^2 + 268*T - 346544
$67$
\( T^{2} - 920T + 159580 \)
T^2 - 920*T + 159580
$71$
\( T^{2} + 656T - 170896 \)
T^2 + 656*T - 170896
$73$
\( T^{2} - 232T - 304064 \)
T^2 - 232*T - 304064
$79$
\( T^{2} + 114 T - 1177731 \)
T^2 + 114*T - 1177731
$83$
\( T^{2} + 8T - 1601764 \)
T^2 + 8*T - 1601764
$89$
\( T^{2} - 852T - 642704 \)
T^2 - 852*T - 642704
$97$
\( T^{2} + 480T - 392400 \)
T^2 + 480*T - 392400
show more
show less