[N,k,chi] = [836,2,Mod(1,836)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(836, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("836.1");
S:= CuspForms(chi, 2);
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
\(2\)
\(-1\)
\(11\)
\(-1\)
\(19\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{6} + 2T_{3}^{5} - 12T_{3}^{4} - 28T_{3}^{3} + 16T_{3}^{2} + 60T_{3} + 27 \)
T3^6 + 2*T3^5 - 12*T3^4 - 28*T3^3 + 16*T3^2 + 60*T3 + 27
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(836))\).
$p$
$F_p(T)$
$2$
\( T^{6} \)
T^6
$3$
\( T^{6} + 2 T^{5} - 12 T^{4} - 28 T^{3} + \cdots + 27 \)
T^6 + 2*T^5 - 12*T^4 - 28*T^3 + 16*T^2 + 60*T + 27
$5$
\( T^{6} - 28 T^{4} - 6 T^{3} + 228 T^{2} + \cdots - 543 \)
T^6 - 28*T^4 - 6*T^3 + 228*T^2 + 48*T - 543
$7$
\( T^{6} - 2 T^{5} - 43 T^{4} + \cdots - 1738 \)
T^6 - 2*T^5 - 43*T^4 + 78*T^3 + 547*T^2 - 760*T - 1738
$11$
\( (T - 1)^{6} \)
(T - 1)^6
$13$
\( T^{6} - 2 T^{5} - 49 T^{4} + \cdots + 2462 \)
T^6 - 2*T^5 - 49*T^4 + 156*T^3 + 475*T^2 - 2404*T + 2462
$17$
\( T^{6} - 12 T^{5} - 18 T^{4} + \cdots - 2592 \)
T^6 - 12*T^5 - 18*T^4 + 480*T^3 - 96*T^2 - 4032*T - 2592
$19$
\( (T - 1)^{6} \)
(T - 1)^6
$23$
\( T^{6} + 2 T^{5} - 75 T^{4} + \cdots - 1584 \)
T^6 + 2*T^5 - 75*T^4 - 120*T^3 + 1044*T^2 + 1104*T - 1584
$29$
\( T^{6} - 4 T^{5} - 69 T^{4} + \cdots - 2682 \)
T^6 - 4*T^5 - 69*T^4 + 174*T^3 + 1263*T^2 - 1056*T - 2682
$31$
\( T^{6} + 20 T^{5} + 88 T^{4} + \cdots - 7593 \)
T^6 + 20*T^5 + 88*T^4 - 524*T^3 - 4984*T^2 - 11390*T - 7593
$37$
\( T^{6} - 22 T^{5} + 67 T^{4} + \cdots + 91824 \)
T^6 - 22*T^5 + 67*T^4 + 1456*T^3 - 10120*T^2 - 608*T + 91824
$41$
\( T^{6} + 2 T^{5} - 159 T^{4} + \cdots + 24912 \)
T^6 + 2*T^5 - 159*T^4 - 444*T^3 + 4725*T^2 + 22344*T + 24912
$43$
\( T^{6} - 10 T^{5} - 25 T^{4} + \cdots + 4900 \)
T^6 - 10*T^5 - 25*T^4 + 470*T^3 - 907*T^2 - 1900*T + 4900
$47$
\( T^{6} - 16 T^{5} - 96 T^{4} + \cdots + 328896 \)
T^6 - 16*T^5 - 96*T^4 + 2496*T^3 - 4032*T^2 - 86592*T + 328896
$53$
\( T^{6} - 12 T^{5} - 96 T^{4} + \cdots - 31104 \)
T^6 - 12*T^5 - 96*T^4 + 1296*T^3 + 912*T^2 - 19584*T - 31104
$59$
\( T^{6} + 14 T^{5} - 81 T^{4} + \cdots + 31536 \)
T^6 + 14*T^5 - 81*T^4 - 1212*T^3 + 900*T^2 + 24048*T + 31536
$61$
\( T^{6} - 12 T^{5} - 214 T^{4} + \cdots + 109728 \)
T^6 - 12*T^5 - 214*T^4 + 2488*T^3 + 10560*T^2 - 124960*T + 109728
$67$
\( T^{6} + 12 T^{5} - 184 T^{4} + \cdots + 253887 \)
T^6 + 12*T^5 - 184*T^4 - 2300*T^3 + 5400*T^2 + 110978*T + 253887
$71$
\( T^{6} + 30 T^{5} + 252 T^{4} + \cdots + 2187 \)
T^6 + 30*T^5 + 252*T^4 + 324*T^3 - 1944*T^2 - 2916*T + 2187
$73$
\( T^{6} - 24 T^{5} - 52 T^{4} + \cdots - 217728 \)
T^6 - 24*T^5 - 52*T^4 + 5296*T^3 - 49680*T^2 + 177920*T - 217728
$79$
\( T^{6} - 370 T^{4} - 1184 T^{3} + \cdots + 428832 \)
T^6 - 370*T^4 - 1184*T^3 + 32136*T^2 + 231872*T + 428832
$83$
\( T^{6} + 14 T^{5} - 135 T^{4} + \cdots - 177642 \)
T^6 + 14*T^5 - 135*T^4 - 1446*T^3 + 7875*T^2 + 37752*T - 177642
$89$
\( T^{6} + 14 T^{5} - 173 T^{4} + \cdots + 19776 \)
T^6 + 14*T^5 - 173*T^4 - 1260*T^3 + 14232*T^2 - 31392*T + 19776
$97$
\( T^{6} + 46 T^{5} + 791 T^{4} + \cdots + 752 \)
T^6 + 46*T^5 + 791*T^4 + 6288*T^3 + 22852*T^2 + 29888*T + 752
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