[N,k,chi] = [2312,4,Mod(1,2312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2312, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2312.1");
S:= CuspForms(chi, 4);
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
\(2\)
\(-1\)
\(17\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{3} - 4T_{3}^{2} - 30T_{3} - 28 \)
T3^3 - 4*T3^2 - 30*T3 - 28
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(2312))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( T^{3} - 4 T^{2} - 30 T - 28 \)
T^3 - 4*T^2 - 30*T - 28
$5$
\( T^{3} - 8 T^{2} - 236 T - 288 \)
T^3 - 8*T^2 - 236*T - 288
$7$
\( T^{3} - 2 T^{2} - 714 T - 3848 \)
T^3 - 2*T^2 - 714*T - 3848
$11$
\( T^{3} - 84 T^{2} + 2026 T - 10972 \)
T^3 - 84*T^2 + 2026*T - 10972
$13$
\( T^{3} + 50 T^{2} + 64 T - 16048 \)
T^3 + 50*T^2 + 64*T - 16048
$17$
\( T^{3} \)
T^3
$19$
\( T^{3} + 224 T^{2} + 15336 T + 322592 \)
T^3 + 224*T^2 + 15336*T + 322592
$23$
\( T^{3} - 234 T^{2} + 18118 T - 463504 \)
T^3 - 234*T^2 + 18118*T - 463504
$29$
\( T^{3} - 72 T^{2} - 23340 T + 1862624 \)
T^3 - 72*T^2 - 23340*T + 1862624
$31$
\( T^{3} - 2 T^{2} - 52450 T + 1252344 \)
T^3 - 2*T^2 - 52450*T + 1252344
$37$
\( T^{3} + 100 T^{2} - 89196 T + 4014352 \)
T^3 + 100*T^2 - 89196*T + 4014352
$41$
\( T^{3} + 218 T^{2} - 66340 T - 7651496 \)
T^3 + 218*T^2 - 66340*T - 7651496
$43$
\( T^{3} - 44 T^{2} - 234152 T - 18647936 \)
T^3 - 44*T^2 - 234152*T - 18647936
$47$
\( T^{3} + 16 T^{2} - 141616 T - 7663872 \)
T^3 + 16*T^2 - 141616*T - 7663872
$53$
\( T^{3} - 462 T^{2} + \cdots + 10502936 \)
T^3 - 462*T^2 - 131316*T + 10502936
$59$
\( T^{3} + 68 T^{2} - 465864 T - 81654208 \)
T^3 + 68*T^2 - 465864*T - 81654208
$61$
\( T^{3} + 460 T^{2} + \cdots - 116249648 \)
T^3 + 460*T^2 - 488892*T - 116249648
$67$
\( T^{3} + 1008 T^{2} + \cdots - 534256128 \)
T^3 + 1008*T^2 - 528624*T - 534256128
$71$
\( T^{3} + 518 T^{2} + \cdots - 93696432 \)
T^3 + 518*T^2 - 192946*T - 93696432
$73$
\( T^{3} + 838 T^{2} + \cdots - 324704504 \)
T^3 + 838*T^2 - 439796*T - 324704504
$79$
\( T^{3} + 1238 T^{2} + \cdots + 7088608 \)
T^3 + 1238*T^2 + 385382*T + 7088608
$83$
\( T^{3} + 1148 T^{2} + \cdots - 158784832 \)
T^3 + 1148*T^2 + 71224*T - 158784832
$89$
\( T^{3} + 2506 T^{2} + \cdots + 456757648 \)
T^3 + 2506*T^2 + 1918096*T + 456757648
$97$
\( T^{3} + 2098 T^{2} + \cdots - 1961875944 \)
T^3 + 2098*T^2 - 468596*T - 1961875944
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