[N,k,chi] = [1148,2,Mod(1,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, 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("1148.1");
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
\(2\)
\(-1\)
\(7\)
\(1\)
\(41\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{5} - 2T_{3}^{4} - 6T_{3}^{3} + 8T_{3}^{2} + 9T_{3} + 1 \)
T3^5 - 2*T3^4 - 6*T3^3 + 8*T3^2 + 9*T3 + 1
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1148))\).
$p$
$F_p(T)$
$2$
\( T^{5} \)
T^5
$3$
\( T^{5} - 2 T^{4} - 6 T^{3} + 8 T^{2} + \cdots + 1 \)
T^5 - 2*T^4 - 6*T^3 + 8*T^2 + 9*T + 1
$5$
\( T^{5} + 3 T^{4} - 9 T^{3} - 12 T^{2} + \cdots - 8 \)
T^5 + 3*T^4 - 9*T^3 - 12*T^2 + 28*T - 8
$7$
\( (T + 1)^{5} \)
(T + 1)^5
$11$
\( T^{5} - 6 T^{4} - 7 T^{3} + 68 T^{2} + \cdots + 24 \)
T^5 - 6*T^4 - 7*T^3 + 68*T^2 - 84*T + 24
$13$
\( T^{5} - 7 T^{4} - 5 T^{3} + 36 T^{2} + \cdots - 27 \)
T^5 - 7*T^4 - 5*T^3 + 36*T^2 + 18*T - 27
$17$
\( T^{5} - T^{4} - 17 T^{3} - 14 T^{2} + \cdots + 1 \)
T^5 - T^4 - 17*T^3 - 14*T^2 + 18*T + 1
$19$
\( T^{5} - 2 T^{4} - 68 T^{3} + \cdots - 3643 \)
T^5 - 2*T^4 - 68*T^3 + 176*T^2 + 1167*T - 3643
$23$
\( T^{5} - 4 T^{4} - 92 T^{3} + \cdots - 5721 \)
T^5 - 4*T^4 - 92*T^3 + 310*T^2 + 2109*T - 5721
$29$
\( T^{5} - 11 T^{4} - 31 T^{3} + \cdots - 216 \)
T^5 - 11*T^4 - 31*T^3 + 400*T^2 + 396*T - 216
$31$
\( T^{5} - 13 T^{4} - 25 T^{3} + \cdots + 1176 \)
T^5 - 13*T^4 - 25*T^3 + 782*T^2 - 2520*T + 1176
$37$
\( T^{5} - 5 T^{4} - 68 T^{3} + \cdots - 1748 \)
T^5 - 5*T^4 - 68*T^3 + 223*T^2 + 670*T - 1748
$41$
\( (T + 1)^{5} \)
(T + 1)^5
$43$
\( T^{5} - 29 T^{4} + 307 T^{3} + \cdots - 2161 \)
T^5 - 29*T^4 + 307*T^3 - 1450*T^2 + 3008*T - 2161
$47$
\( T^{5} - 7 T^{4} - 74 T^{3} + \cdots - 1532 \)
T^5 - 7*T^4 - 74*T^3 + 289*T^2 + 1010*T - 1532
$53$
\( T^{5} - 21 T^{4} + 89 T^{3} + \cdots - 152 \)
T^5 - 21*T^4 + 89*T^3 + 240*T^2 - 284*T - 152
$59$
\( T^{5} - 3 T^{4} - 263 T^{3} + \cdots - 55448 \)
T^5 - 3*T^4 - 263*T^3 + 586*T^2 + 14408*T - 55448
$61$
\( T^{5} + 8 T^{4} - 167 T^{3} + \cdots + 11944 \)
T^5 + 8*T^4 - 167*T^3 - 878*T^2 + 6936*T + 11944
$67$
\( T^{5} - 3 T^{4} - 345 T^{3} + \cdots + 51208 \)
T^5 - 3*T^4 - 345*T^3 + 108*T^2 + 28924*T + 51208
$71$
\( T^{5} - 22 T^{4} - 203 T^{3} + \cdots - 308544 \)
T^5 - 22*T^4 - 203*T^3 + 5596*T^2 + 6336*T - 308544
$73$
\( T^{5} + 16 T^{4} - 27 T^{3} + \cdots + 2664 \)
T^5 + 16*T^4 - 27*T^3 - 514*T^2 - 192*T + 2664
$79$
\( T^{5} - 4 T^{4} - 288 T^{3} + \cdots - 100896 \)
T^5 - 4*T^4 - 288*T^3 + 1408*T^2 + 17616*T - 100896
$83$
\( T^{5} + 6 T^{4} - 89 T^{3} + \cdots + 5272 \)
T^5 + 6*T^4 - 89*T^3 - 326*T^2 + 1604*T + 5272
$89$
\( T^{5} + 20 T^{4} + 46 T^{3} + \cdots - 5297 \)
T^5 + 20*T^4 + 46*T^3 - 818*T^2 - 4239*T - 5297
$97$
\( T^{5} + 24 T^{4} - 122 T^{3} + \cdots - 122173 \)
T^5 + 24*T^4 - 122*T^3 - 6952*T^2 - 55351*T - 122173
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