[N,k,chi] = [12,24,Mod(1,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.1");
S:= CuspForms(chi, 24);
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 \(\beta = 8640\sqrt{18699409}\).
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
\( T_{5}^{2} - 73907100T_{5} - 30338544483900 \)
T5^2 - 73907100*T5 - 30338544483900
acting on \(S_{24}^{\mathrm{new}}(\Gamma_0(12))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( (T - 177147)^{2} \)
(T - 177147)^2
$5$
\( T^{2} - 73907100 T - 30338544483900 \)
T^2 - 73907100*T - 30338544483900
$7$
\( T^{2} + 1531228496 T - 73\!\cdots\!96 \)
T^2 + 1531228496*T - 73900636261991784896
$11$
\( T^{2} - 856002839112 T - 24\!\cdots\!64 \)
T^2 - 856002839112*T - 24376737219045662913264
$13$
\( T^{2} - 1540387619020 T - 82\!\cdots\!00 \)
T^2 - 1540387619020*T - 8297306963765112901310300
$17$
\( T^{2} - 187790553857124 T - 91\!\cdots\!56 \)
T^2 - 187790553857124*T - 9137335368149756882668125756
$19$
\( T^{2} - 355556665589560 T - 27\!\cdots\!00 \)
T^2 - 355556665589560*T - 27507271858198755956169513200
$23$
\( T^{2} + \cdots - 34\!\cdots\!76 \)
T^2 + 1138656565833264*T - 34630098679180867646980544458176
$29$
\( T^{2} + \cdots - 39\!\cdots\!64 \)
T^2 - 49048810194760812*T - 3991578504548112970528881739435164
$31$
\( T^{2} + \cdots - 17\!\cdots\!24 \)
T^2 - 112487054427202048*T - 17188638707689027451523744337793024
$37$
\( T^{2} + \cdots + 53\!\cdots\!76 \)
T^2 - 595791580295773852*T + 53433094130746254182827158486055876
$41$
\( T^{2} + \cdots - 11\!\cdots\!00 \)
T^2 - 4140263347824516660*T - 11960451868594977295777484294174257500
$43$
\( T^{2} + \cdots + 22\!\cdots\!84 \)
T^2 - 12484976728080021256*T + 22073611136265696894776295904797907984
$47$
\( T^{2} + \cdots + 39\!\cdots\!24 \)
T^2 - 40677363763116162336*T + 393534100966897043357103780146203578624
$53$
\( T^{2} + \cdots + 87\!\cdots\!96 \)
T^2 - 134517513727968765372*T + 872026785456162083610870646672871614596
$59$
\( T^{2} + \cdots - 48\!\cdots\!04 \)
T^2 - 111073075668542138472*T - 48247745148042116929264678026987198862704
$61$
\( T^{2} + \cdots + 36\!\cdots\!44 \)
T^2 - 381734226285491238124*T + 36002165738086586874474317714114477305444
$67$
\( T^{2} + \cdots + 19\!\cdots\!04 \)
T^2 + 1195543108943866574504*T + 193623132946185263102733106042953620181904
$71$
\( T^{2} + \cdots + 70\!\cdots\!00 \)
T^2 + 5312805341183533265040*T + 7047686472425845755864316420118580775310400
$73$
\( T^{2} + \cdots + 15\!\cdots\!36 \)
T^2 + 3748075384168719094412*T + 1561726486386110766759738028049988014636836
$79$
\( T^{2} + \cdots + 46\!\cdots\!64 \)
T^2 + 6657760961801696050016*T + 4697666626211003983037230925465970046814464
$83$
\( T^{2} + \cdots - 30\!\cdots\!16 \)
T^2 - 4879709035701866972856*T - 304279595357609123006451155939351542682482416
$89$
\( T^{2} + \cdots - 31\!\cdots\!00 \)
T^2 - 15150179215931983754580*T - 310146726759226320768851684804022752812566300
$97$
\( T^{2} + \cdots - 59\!\cdots\!84 \)
T^2 - 91184235652282349450308*T - 599064905945467484325220910839854347678421884
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