[N,k,chi] = [63,12,Mod(1,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.1");
S:= CuspForms(chi, 12);
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
\(3\)
\(-1\)
\(7\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} + 77T_{2}^{2} - 2854T_{2} - 225104 \)
T2^3 + 77*T2^2 - 2854*T2 - 225104
acting on \(S_{12}^{\mathrm{new}}(\Gamma_0(63))\).
$p$
$F_p(T)$
$2$
\( T^{3} + 77 T^{2} - 2854 T - 225104 \)
T^3 + 77*T^2 - 2854*T - 225104
$3$
\( T^{3} \)
T^3
$5$
\( T^{3} + 5026 T^{2} + \cdots + 68056486400 \)
T^3 + 5026*T^2 - 95074240*T + 68056486400
$7$
\( (T + 16807)^{3} \)
(T + 16807)^3
$11$
\( T^{3} - 1039052 T^{2} + \cdots + 33\!\cdots\!52 \)
T^3 - 1039052*T^2 + 106979986688*T + 33609013371959552
$13$
\( T^{3} + 1881222 T^{2} + \cdots - 91\!\cdots\!44 \)
T^3 + 1881222*T^2 + 788070396288*T - 91621167814810144
$17$
\( T^{3} + 15797334 T^{2} + \cdots + 62\!\cdots\!52 \)
T^3 + 15797334*T^2 + 65878431119388*T + 62094891277796309352
$19$
\( T^{3} - 12340356 T^{2} + \cdots - 43\!\cdots\!00 \)
T^3 - 12340356*T^2 + 42087546949572*T - 43257850059191958400
$23$
\( T^{3} + 7276752 T^{2} + \cdots - 42\!\cdots\!72 \)
T^3 + 7276752*T^2 - 2970108112280832*T - 42000810761587863785472
$29$
\( T^{3} - 126853406 T^{2} + \cdots + 25\!\cdots\!60 \)
T^3 - 126853406*T^2 - 6075574735083268*T + 257492653332388131607160
$31$
\( T^{3} - 162184512 T^{2} + \cdots + 14\!\cdots\!00 \)
T^3 - 162184512*T^2 - 15226270486760880*T + 1465000411106695377801600
$37$
\( T^{3} - 567121338 T^{2} + \cdots + 13\!\cdots\!84 \)
T^3 - 567121338*T^2 + 37192066051084380*T + 1355966501442959154930984
$41$
\( T^{3} + 893682734 T^{2} + \cdots - 46\!\cdots\!72 \)
T^3 + 893682734*T^2 - 678233415148671172*T - 464073340153702976639663672
$43$
\( T^{3} - 460197828 T^{2} + \cdots + 22\!\cdots\!64 \)
T^3 - 460197828*T^2 - 136035151991724288*T + 22192202517256977014616064
$47$
\( T^{3} + 2723825664 T^{2} + \cdots + 21\!\cdots\!48 \)
T^3 + 2723825664*T^2 + 1472056144713292752*T + 213337834797513917980798848
$53$
\( T^{3} + 93426522 T^{2} + \cdots + 36\!\cdots\!88 \)
T^3 + 93426522*T^2 - 4921626065139502452*T + 3601867649193243158200896888
$59$
\( T^{3} + 5899174428 T^{2} + \cdots - 66\!\cdots\!60 \)
T^3 + 5899174428*T^2 + 5229356802745684356*T - 665714447773103511228065760
$61$
\( T^{3} - 2106807738 T^{2} + \cdots + 35\!\cdots\!68 \)
T^3 - 2106807738*T^2 - 83940021540015643872*T + 359130074235011116699419459968
$67$
\( T^{3} + 27027285348 T^{2} + \cdots + 23\!\cdots\!64 \)
T^3 + 27027285348*T^2 + 150600418325062747056*T + 237600491562613391025602243264
$71$
\( T^{3} + 16564049928 T^{2} + \cdots - 61\!\cdots\!92 \)
T^3 + 16564049928*T^2 + 5230192110719348736*T - 615400877083852929330713198592
$73$
\( T^{3} - 6036803934 T^{2} + \cdots - 15\!\cdots\!96 \)
T^3 - 6036803934*T^2 - 357356395767570386580*T - 1521334678544426666075814337896
$79$
\( T^{3} + 54895016736 T^{2} + \cdots + 29\!\cdots\!20 \)
T^3 + 54895016736*T^2 + 827674117716961294656*T + 2997703717247628759407795307520
$83$
\( T^{3} + 123561203892 T^{2} + \cdots + 57\!\cdots\!72 \)
T^3 + 123561203892*T^2 + 4760086993725097788516*T + 57474159834699517912111012159872
$89$
\( T^{3} - 91648411106 T^{2} + \cdots + 89\!\cdots\!00 \)
T^3 - 91648411106*T^2 + 366693279130475847212*T + 89812643222996426673109682445800
$97$
\( T^{3} + 71237114634 T^{2} + \cdots - 27\!\cdots\!84 \)
T^3 + 71237114634*T^2 - 2516208328294853538276*T - 27238273989535528786186908119784
show more
show less