[N,k,chi] = [165,4,Mod(1,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, 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("165.1");
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
\(3\)
\(-1\)
\(5\)
\(1\)
\(11\)
\(1\)
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 \(S_{4}^{\mathrm{new}}(\Gamma_0(165))\).
$p$
$F_p(T)$
$2$
\( T^{2} + T - 4 \)
T^2 + T - 4
$3$
\( (T - 3)^{2} \)
(T - 3)^2
$5$
\( (T + 5)^{2} \)
(T + 5)^2
$7$
\( T^{2} + 4T - 64 \)
T^2 + 4*T - 64
$11$
\( (T + 11)^{2} \)
(T + 11)^2
$13$
\( T^{2} + 90T + 2008 \)
T^2 + 90*T + 2008
$17$
\( T^{2} + 16T - 8164 \)
T^2 + 16*T - 8164
$19$
\( T^{2} + 170T + 5168 \)
T^2 + 170*T + 5168
$23$
\( T^{2} + 124T - 11456 \)
T^2 + 124*T - 11456
$29$
\( T^{2} + 158T + 1328 \)
T^2 + 158*T + 1328
$31$
\( T^{2} - 60T + 288 \)
T^2 - 60*T + 288
$37$
\( T^{2} + 372T - 18716 \)
T^2 + 372*T - 18716
$41$
\( T^{2} - 38T - 100432 \)
T^2 - 38*T - 100432
$43$
\( T^{2} + 516T + 1216 \)
T^2 + 516*T + 1216
$47$
\( T^{2} - 224T - 185744 \)
T^2 - 224*T - 185744
$53$
\( T^{2} - 472T - 107572 \)
T^2 - 472*T - 107572
$59$
\( T^{2} - 248T - 229424 \)
T^2 - 248*T - 229424
$61$
\( T^{2} - 72T - 561812 \)
T^2 - 72*T - 561812
$67$
\( T^{2} + 744T + 137296 \)
T^2 + 744*T + 137296
$71$
\( T^{2} - 2060 T + 1052672 \)
T^2 - 2060*T + 1052672
$73$
\( T^{2} + 486T + 44752 \)
T^2 + 486*T + 44752
$79$
\( T^{2} - 642T - 294912 \)
T^2 - 642*T - 294912
$83$
\( T^{2} + 286T - 750824 \)
T^2 + 286*T - 750824
$89$
\( T^{2} - 244T - 54748 \)
T^2 - 244*T - 54748
$97$
\( T^{2} + 168T - 771476 \)
T^2 + 168*T - 771476
show more
show less