[N,k,chi] = [162,6,Mod(1,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, 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("162.1");
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 \(\beta = 6\sqrt{6}\).
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
\(2\)
\(-1\)
\(3\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{2} + 54T_{5} - 135 \)
T5^2 + 54*T5 - 135
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(162))\).
$p$
$F_p(T)$
$2$
\( (T - 4)^{2} \)
(T - 4)^2
$3$
\( T^{2} \)
T^2
$5$
\( T^{2} + 54T - 135 \)
T^2 + 54*T - 135
$7$
\( T^{2} + 74T + 1153 \)
T^2 + 74*T + 1153
$11$
\( T^{2} + 78T - 397863 \)
T^2 + 78*T - 397863
$13$
\( T^{2} + 1106 T + 219409 \)
T^2 + 1106*T + 219409
$17$
\( T^{2} + 492 T - 1848060 \)
T^2 + 492*T - 1848060
$19$
\( T^{2} + 1640 T - 2648816 \)
T^2 + 1640*T - 2648816
$23$
\( T^{2} + 5538 T + 7532361 \)
T^2 + 5538*T + 7532361
$29$
\( T^{2} + 3894 T + 469593 \)
T^2 + 3894*T + 469593
$31$
\( T^{2} + 4718 T - 35307719 \)
T^2 + 4718*T - 35307719
$37$
\( T^{2} + 4796 T - 141621212 \)
T^2 + 4796*T - 141621212
$41$
\( T^{2} - 15354 T + 58893993 \)
T^2 - 15354*T + 58893993
$43$
\( T^{2} + 32858 T + 254513617 \)
T^2 + 32858*T + 254513617
$47$
\( T^{2} - 24954 T + 142283313 \)
T^2 - 24954*T + 142283313
$53$
\( T^{2} - 16332 T + 59839812 \)
T^2 - 16332*T + 59839812
$59$
\( T^{2} - 21966 T + 99734553 \)
T^2 - 21966*T + 99734553
$61$
\( T^{2} + 3050 T - 105947399 \)
T^2 + 3050*T - 105947399
$67$
\( T^{2} + 36758 T - 265336415 \)
T^2 + 36758*T - 265336415
$71$
\( T^{2} - 73848 T + 665096112 \)
T^2 - 73848*T + 665096112
$73$
\( T^{2} + 51188 T + 491562436 \)
T^2 + 51188*T + 491562436
$79$
\( T^{2} - 14926 T - 52271015 \)
T^2 - 14926*T - 52271015
$83$
\( T^{2} - 90762 T + 2054767617 \)
T^2 - 90762*T + 2054767617
$89$
\( T^{2} - 9300 T - 7978887036 \)
T^2 - 9300*T - 7978887036
$97$
\( T^{2} - 30262 T - 9106027655 \)
T^2 - 30262*T - 9106027655
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