[N,k,chi] = [252,12,Mod(1,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("252.1");
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
\(2\)
\(-1\)
\(3\)
\(-1\)
\(7\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{3} + 4762T_{5}^{2} - 7301200T_{5} - 6467756800 \)
T5^3 + 4762*T5^2 - 7301200*T5 - 6467756800
acting on \(S_{12}^{\mathrm{new}}(\Gamma_0(252))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( T^{3} \)
T^3
$5$
\( T^{3} + 4762 T^{2} + \cdots - 6467756800 \)
T^3 + 4762*T^2 - 7301200*T - 6467756800
$7$
\( (T + 16807)^{3} \)
(T + 16807)^3
$11$
\( T^{3} + 80468 T^{2} + \cdots - 29\!\cdots\!00 \)
T^3 + 80468*T^2 - 815588318080*T - 294809610447584000
$13$
\( T^{3} - 996546 T^{2} + \cdots + 54\!\cdots\!44 \)
T^3 - 996546*T^2 - 4717345852944*T + 5407554491957120544
$17$
\( T^{3} - 7924090 T^{2} + \cdots + 42\!\cdots\!60 \)
T^3 - 7924090*T^2 - 57208581965284*T + 427140694254213294760
$19$
\( T^{3} + 15261732 T^{2} + \cdots - 41\!\cdots\!52 \)
T^3 + 15261732*T^2 - 287910767556876*T - 4161641054656218119552
$23$
\( T^{3} - 61428352 T^{2} + \cdots + 88\!\cdots\!52 \)
T^3 - 61428352*T^2 + 662677644479744*T + 8838932682335394045952
$29$
\( T^{3} - 160359182 T^{2} + \cdots + 11\!\cdots\!12 \)
T^3 - 160359182*T^2 - 11503932465672196*T + 1142250768238935251782712
$31$
\( T^{3} + 342148464 T^{2} + \cdots + 98\!\cdots\!64 \)
T^3 + 342148464*T^2 + 34874264214323856*T + 988088453979523050478464
$37$
\( T^{3} + 722039190 T^{2} + \cdots + 19\!\cdots\!80 \)
T^3 + 722039190*T^2 + 98970719532612444*T + 1937405187637650527048680
$41$
\( T^{3} + 285288606 T^{2} + \cdots + 44\!\cdots\!84 \)
T^3 + 285288606*T^2 - 391664836950458436*T + 4446693975126835182059784
$43$
\( T^{3} + 476523612 T^{2} + \cdots - 80\!\cdots\!20 \)
T^3 + 476523612*T^2 - 1264745362339452288*T - 802386638806078952465899520
$47$
\( T^{3} + 1225105680 T^{2} + \cdots - 93\!\cdots\!44 \)
T^3 + 1225105680*T^2 - 2871416393017364592*T - 93207896438035598991356544
$53$
\( T^{3} + 4030571514 T^{2} + \cdots - 90\!\cdots\!00 \)
T^3 + 4030571514*T^2 - 1772456658198002676*T - 90774464121841155647445000
$59$
\( T^{3} + 5222175892 T^{2} + \cdots - 26\!\cdots\!80 \)
T^3 + 5222175892*T^2 - 49396135630643289868*T - 266110243518518116396137117280
$61$
\( T^{3} - 5684837106 T^{2} + \cdots + 76\!\cdots\!00 \)
T^3 - 5684837106*T^2 - 121252337048237308272*T + 761159026826852603790252499200
$67$
\( T^{3} - 2837154348 T^{2} + \cdots - 31\!\cdots\!20 \)
T^3 - 2837154348*T^2 - 142131811980539784144*T - 31580428628022803163426541120
$71$
\( T^{3} - 16928678200 T^{2} + \cdots - 31\!\cdots\!00 \)
T^3 - 16928678200*T^2 - 168055217656538028544*T - 317538386105074102390695526400
$73$
\( T^{3} + 14560325442 T^{2} + \cdots - 66\!\cdots\!60 \)
T^3 + 14560325442*T^2 - 444961290659618603028*T - 660730901996849829250061565160
$79$
\( T^{3} + 32832340032 T^{2} + \cdots - 50\!\cdots\!96 \)
T^3 + 32832340032*T^2 - 1707012034409794345920*T - 50831085178597521063415329156096
$83$
\( T^{3} - 115451875348 T^{2} + \cdots - 30\!\cdots\!00 \)
T^3 - 115451875348*T^2 + 3875708821796839051412*T - 30270941210891631537401463555200
$89$
\( T^{3} - 15661530882 T^{2} + \cdots + 42\!\cdots\!20 \)
T^3 - 15661530882*T^2 - 4522294548005951307348*T + 42692806180865921782184105103720
$97$
\( T^{3} - 40693412742 T^{2} + \cdots + 44\!\cdots\!56 \)
T^3 - 40693412742*T^2 - 2142831658767110928612*T + 44542663304231263373347971943256
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