[N,k,chi] = [1156,4,Mod(1,1156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1156, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1156.1");
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 subspace can be constructed as the kernel of the linear operator
\( T_{3}^{6} - 62T_{3}^{4} + 700T_{3}^{2} - 648 \)
T3^6 - 62*T3^4 + 700*T3^2 - 648
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1156))\).
$p$
$F_p(T)$
$2$
\( T^{6} \)
T^6
$3$
\( T^{6} - 62 T^{4} + 700 T^{2} + \cdots - 648 \)
T^6 - 62*T^4 + 700*T^2 - 648
$5$
\( T^{6} - 572 T^{4} + 81796 T^{2} + \cdots - 2562848 \)
T^6 - 572*T^4 + 81796*T^2 - 2562848
$7$
\( T^{6} - 660 T^{4} + 115588 T^{2} + \cdots - 2179872 \)
T^6 - 660*T^4 + 115588*T^2 - 2179872
$11$
\( T^{6} - 5278 T^{4} + \cdots - 143888648 \)
T^6 - 5278*T^4 + 2248892*T^2 - 143888648
$13$
\( (T^{3} + 46 T^{2} + 316 T - 3896)^{2} \)
(T^3 + 46*T^2 + 316*T - 3896)^2
$17$
\( T^{6} \)
T^6
$19$
\( (T^{3} - 60 T^{2} - 15500 T + 194000)^{2} \)
(T^3 - 60*T^2 - 15500*T + 194000)^2
$23$
\( T^{6} - 12300 T^{4} + \cdots - 32772608 \)
T^6 - 12300*T^4 + 34480164*T^2 - 32772608
$29$
\( T^{6} - 121116 T^{4} + \cdots - 56691570507552 \)
T^6 - 121116*T^4 + 4682154820*T^2 - 56691570507552
$31$
\( T^{6} - 48692 T^{4} + \cdots - 276333674528 \)
T^6 - 48692*T^4 + 378955972*T^2 - 276333674528
$37$
\( T^{6} - 262196 T^{4} + \cdots - 294101549568 \)
T^6 - 262196*T^4 + 14990458084*T^2 - 294101549568
$41$
\( T^{6} + \cdots - 332174590800392 \)
T^6 - 317318*T^4 + 25324472332*T^2 - 332174590800392
$43$
\( (T^{3} + 222 T^{2} - 124844 T - 17200936)^{2} \)
(T^3 + 222*T^2 - 124844*T - 17200936)^2
$47$
\( (T^{3} + 664 T^{2} - 5632 T - 42870784)^{2} \)
(T^3 + 664*T^2 - 5632*T - 42870784)^2
$53$
\( (T^{3} - 526 T^{2} + 90448 T - 5087584)^{2} \)
(T^3 - 526*T^2 + 90448*T - 5087584)^2
$59$
\( (T^{3} + 322 T^{2} - 226348 T - 71289688)^{2} \)
(T^3 + 322*T^2 - 226348*T - 71289688)^2
$61$
\( T^{6} + \cdots - 105473055616128 \)
T^6 - 210292*T^4 + 12070112932*T^2 - 105473055616128
$67$
\( (T^{3} - 350 T^{2} - 212128 T + 63674784)^{2} \)
(T^3 - 350*T^2 - 212128*T + 63674784)^2
$71$
\( T^{6} - 391852 T^{4} + \cdots - 10\!\cdots\!68 \)
T^6 - 391852*T^4 + 42565103012*T^2 - 1013213645706368
$73$
\( T^{6} - 1471142 T^{4} + \cdots - 61\!\cdots\!28 \)
T^6 - 1471142*T^4 + 627778672780*T^2 - 61140679423125128
$79$
\( T^{6} - 2530604 T^{4} + \cdots - 12\!\cdots\!68 \)
T^6 - 2530604*T^4 + 1588483652580*T^2 - 12243205510023168
$83$
\( (T^{3} + 22 T^{2} - 215116 T - 11907208)^{2} \)
(T^3 + 22*T^2 - 215116*T - 11907208)^2
$89$
\( (T^{3} + 1620 T^{2} + 546948 T - 31482432)^{2} \)
(T^3 + 1620*T^2 + 546948*T - 31482432)^2
$97$
\( T^{6} - 5063638 T^{4} + \cdots - 41\!\cdots\!68 \)
T^6 - 5063638*T^4 + 8180556980044*T^2 - 4185001526692605768
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