[N,k,chi] = [23,6,Mod(1,23)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(23, 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("23.1");
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
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
\(23\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} + 4T_{2}^{2} - 48T_{2} - 8 \)
T2^3 + 4*T2^2 - 48*T2 - 8
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(23))\).
$p$
$F_p(T)$
$2$
\( T^{3} + 4 T^{2} - 48 T - 8 \)
T^3 + 4*T^2 - 48*T - 8
$3$
\( T^{3} + 20 T^{2} - 225 T - 360 \)
T^3 + 20*T^2 - 225*T - 360
$5$
\( T^{3} + 58 T^{2} + 668 T - 3504 \)
T^3 + 58*T^2 + 668*T - 3504
$7$
\( T^{3} + 282 T^{2} + 13108 T + 116944 \)
T^3 + 282*T^2 + 13108*T + 116944
$11$
\( T^{3} - 136 T^{2} - 43688 T + 840152 \)
T^3 - 136*T^2 - 43688*T + 840152
$13$
\( T^{3} + 1116 T^{2} + \cdots - 255615102 \)
T^3 + 1116*T^2 - 71523*T - 255615102
$17$
\( T^{3} + 896 T^{2} + \cdots + 220718408 \)
T^3 + 896*T^2 - 1509728*T + 220718408
$19$
\( T^{3} - 1654 T^{2} + \cdots + 460771768 \)
T^3 - 1654*T^2 - 1853428*T + 460771768
$23$
\( (T + 529)^{3} \)
(T + 529)^3
$29$
\( T^{3} + 844 T^{2} + \cdots - 33789223458 \)
T^3 + 844*T^2 - 28435563*T - 33789223458
$31$
\( T^{3} + 3020 T^{2} + \cdots - 117638912880 \)
T^3 + 3020*T^2 - 35926785*T - 117638912880
$37$
\( T^{3} - 8938 T^{2} + \cdots + 1048082031344 \)
T^3 - 8938*T^2 - 120598692*T + 1048082031344
$41$
\( T^{3} + 12792 T^{2} + \cdots - 1564944049486 \)
T^3 + 12792*T^2 - 123863687*T - 1564944049486
$43$
\( T^{3} + 16730 T^{2} + \cdots - 95315904000 \)
T^3 + 16730*T^2 - 105823200*T - 95315904000
$47$
\( T^{3} - 22500 T^{2} + \cdots + 916008439440 \)
T^3 - 22500*T^2 + 52960375*T + 916008439440
$53$
\( T^{3} - 17108 T^{2} + \cdots + 7849670295504 \)
T^3 - 17108*T^2 - 1075194292*T + 7849670295504
$59$
\( T^{3} - 54176 T^{2} + \cdots - 1725012447168 \)
T^3 - 54176*T^2 + 622993472*T - 1725012447168
$61$
\( T^{3} + 71324 T^{2} + \cdots + 11439907465152 \)
T^3 + 71324*T^2 + 1604797652*T + 11439907465152
$67$
\( T^{3} + 62960 T^{2} + \cdots - 11971711378840 \)
T^3 + 62960*T^2 - 64685160*T - 11971711378840
$71$
\( T^{3} - 98400 T^{2} + \cdots - 24837760695040 \)
T^3 - 98400*T^2 + 2953967755*T - 24837760695040
$73$
\( T^{3} + 81772 T^{2} + \cdots + 7199078503954 \)
T^3 + 81772*T^2 + 1671592593*T + 7199078503954
$79$
\( T^{3} + \cdots + 235690469012368 \)
T^3 - 58224*T^2 - 4055859548*T + 235690469012368
$83$
\( T^{3} + \cdots - 297029282761704 \)
T^3 - 9892*T^2 - 9346901032*T - 297029282761704
$89$
\( T^{3} + \cdots + 125799322340896 \)
T^3 - 27542*T^2 - 3785341592*T + 125799322340896
$97$
\( T^{3} + \cdots + 693755159518744 \)
T^3 + 273672*T^2 + 24254545128*T + 693755159518744
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