[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
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
\(3\)
\(-1\)
\(11\)
\(1\)
\(61\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{5} - 2T_{2}^{4} - 3T_{2}^{3} + 4T_{2}^{2} + 2T_{2} - 1 \)
T2^5 - 2*T2^4 - 3*T2^3 + 4*T2^2 + 2*T2 - 1
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6039))\).
$p$
$F_p(T)$
$2$
\( T^{5} - 2 T^{4} - 3 T^{3} + 4 T^{2} + \cdots - 1 \)
T^5 - 2*T^4 - 3*T^3 + 4*T^2 + 2*T - 1
$3$
\( T^{5} \)
T^5
$5$
\( T^{5} - 2 T^{4} - 3 T^{3} + 6 T^{2} + \cdots - 1 \)
T^5 - 2*T^4 - 3*T^3 + 6*T^2 - 1
$7$
\( T^{5} + T^{4} - 14 T^{3} - T^{2} + 37 T - 23 \)
T^5 + T^4 - 14*T^3 - T^2 + 37*T - 23
$11$
\( (T + 1)^{5} \)
(T + 1)^5
$13$
\( T^{5} + 10 T^{4} + 34 T^{3} + 41 T^{2} + \cdots - 23 \)
T^5 + 10*T^4 + 34*T^3 + 41*T^2 - 2*T - 23
$17$
\( T^{5} - 3 T^{4} - T^{3} + 5 T^{2} - 1 \)
T^5 - 3*T^4 - T^3 + 5*T^2 - 1
$19$
\( T^{5} + 13 T^{4} + 49 T^{3} + 36 T^{2} + \cdots - 5 \)
T^5 + 13*T^4 + 49*T^3 + 36*T^2 - 47*T - 5
$23$
\( T^{5} - 35 T^{3} - 101 T^{2} + \cdots + 59 \)
T^5 - 35*T^3 - 101*T^2 - 49*T + 59
$29$
\( T^{5} - 7 T^{4} - 67 T^{3} + \cdots + 2885 \)
T^5 - 7*T^4 - 67*T^3 + 806*T^2 - 2681*T + 2885
$31$
\( T^{5} + 13 T^{4} + 8 T^{3} - 175 T^{2} + \cdots + 313 \)
T^5 + 13*T^4 + 8*T^3 - 175*T^2 + 39*T + 313
$37$
\( T^{5} + 6 T^{4} - 32 T^{3} - 139 T^{2} + \cdots + 97 \)
T^5 + 6*T^4 - 32*T^3 - 139*T^2 + 308*T + 97
$41$
\( T^{5} - 9 T^{4} + T^{3} + 122 T^{2} + \cdots + 43 \)
T^5 - 9*T^4 + T^3 + 122*T^2 - 199*T + 43
$43$
\( T^{5} - 2 T^{4} - 66 T^{3} + \cdots - 1037 \)
T^5 - 2*T^4 - 66*T^3 + 247*T^2 + 228*T - 1037
$47$
\( T^{5} - 3 T^{4} - 22 T^{3} + 107 T^{2} + \cdots + 17 \)
T^5 - 3*T^4 - 22*T^3 + 107*T^2 - 129*T + 17
$53$
\( T^{5} + 3 T^{4} - 130 T^{3} + \cdots - 2347 \)
T^5 + 3*T^4 - 130*T^3 - 29*T^2 + 3077*T - 2347
$59$
\( T^{5} - 14 T^{4} + 27 T^{3} + \cdots - 655 \)
T^5 - 14*T^4 + 27*T^3 + 309*T^2 - 989*T - 655
$61$
\( (T - 1)^{5} \)
(T - 1)^5
$67$
\( T^{5} + 5 T^{4} - 86 T^{3} + \cdots + 1249 \)
T^5 + 5*T^4 - 86*T^3 - 470*T^2 - 155*T + 1249
$71$
\( T^{5} + 3 T^{4} - 73 T^{3} + 259 T^{2} + \cdots + 149 \)
T^5 + 3*T^4 - 73*T^3 + 259*T^2 - 340*T + 149
$73$
\( T^{5} + 4 T^{4} - 118 T^{3} + \cdots + 431 \)
T^5 + 4*T^4 - 118*T^3 - 99*T^2 + 818*T + 431
$79$
\( T^{5} + 27 T^{4} + 259 T^{3} + \cdots + 1285 \)
T^5 + 27*T^4 + 259*T^3 + 1076*T^2 + 1959*T + 1285
$83$
\( T^{5} - 3 T^{4} - 143 T^{3} + \cdots - 3457 \)
T^5 - 3*T^4 - 143*T^3 + 718*T^2 + 1119*T - 3457
$89$
\( T^{5} - 12 T^{4} - 75 T^{3} + \cdots - 3995 \)
T^5 - 12*T^4 - 75*T^3 + 741*T^2 - 253*T - 3995
$97$
\( T^{5} + 5 T^{4} - 227 T^{3} + \cdots + 62147 \)
T^5 + 5*T^4 - 227*T^3 - 1362*T^2 + 9859*T + 62147
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