[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
\( T_{3}^{5} - 2T_{3}^{4} - 8T_{3}^{3} + 10T_{3}^{2} + 13T_{3} - 11 \)
T3^5 - 2*T3^4 - 8*T3^3 + 10*T3^2 + 13*T3 - 11
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1148))\).
$p$
$F_p(T)$
$2$
\( T^{5} \)
T^5
$3$
\( T^{5} - 2 T^{4} - 8 T^{3} + 10 T^{2} + \cdots - 11 \)
T^5 - 2*T^4 - 8*T^3 + 10*T^2 + 13*T - 11
$5$
\( T^{5} - 3 T^{4} - 9 T^{3} + 20 T^{2} + \cdots - 24 \)
T^5 - 3*T^4 - 9*T^3 + 20*T^2 + 12*T - 24
$7$
\( (T - 1)^{5} \)
(T - 1)^5
$11$
\( T^{5} - 21 T^{3} + 4 T^{2} + 84 T - 72 \)
T^5 - 21*T^3 + 4*T^2 + 84*T - 72
$13$
\( T^{5} - 7 T^{4} + 7 T^{3} + 38 T^{2} + \cdots + 29 \)
T^5 - 7*T^4 + 7*T^3 + 38*T^2 - 80*T + 29
$17$
\( T^{5} + 3 T^{4} - 45 T^{3} - 72 T^{2} + \cdots + 81 \)
T^5 + 3*T^4 - 45*T^3 - 72*T^2 + 540*T + 81
$19$
\( T^{5} - 10 T^{4} + 22 T^{3} + 30 T^{2} + \cdots - 3 \)
T^5 - 10*T^4 + 22*T^3 + 30*T^2 - 81*T - 3
$23$
\( T^{5} - 12 T^{4} + 48 T^{3} - 70 T^{2} + \cdots + 3 \)
T^5 - 12*T^4 + 48*T^3 - 70*T^2 + 21*T + 3
$29$
\( T^{5} + 3 T^{4} - 21 T^{3} - 64 T^{2} + \cdots + 264 \)
T^5 + 3*T^4 - 21*T^3 - 64*T^2 + 84*T + 264
$31$
\( T^{5} - 7 T^{4} + 7 T^{3} + 26 T^{2} + \cdots + 8 \)
T^5 - 7*T^4 + 7*T^3 + 26*T^2 - 32*T + 8
$37$
\( T^{5} - T^{4} - 56 T^{3} - 145 T^{2} + \cdots + 188 \)
T^5 - T^4 - 56*T^3 - 145*T^2 + 10*T + 188
$41$
\( (T - 1)^{5} \)
(T - 1)^5
$43$
\( T^{5} - 13 T^{4} + 19 T^{3} + \cdots - 593 \)
T^5 - 13*T^4 + 19*T^3 + 190*T^2 - 112*T - 593
$47$
\( T^{5} - 9 T^{4} - 66 T^{3} + 107 T^{2} + \cdots + 12 \)
T^5 - 9*T^4 - 66*T^3 + 107*T^2 + 78*T + 12
$53$
\( T^{5} + 3 T^{4} - 9 T^{3} - 20 T^{2} + \cdots + 24 \)
T^5 + 3*T^4 - 9*T^3 - 20*T^2 + 12*T + 24
$59$
\( T^{5} + 3 T^{4} - 87 T^{3} - 178 T^{2} + \cdots - 792 \)
T^5 + 3*T^4 - 87*T^3 - 178*T^2 + 1176*T - 792
$61$
\( T^{5} - 16 T^{4} - 131 T^{3} + \cdots + 35992 \)
T^5 - 16*T^4 - 131*T^3 + 3634*T^2 - 21064*T + 35992
$67$
\( T^{5} - 19 T^{4} + 25 T^{3} + \cdots - 904 \)
T^5 - 19*T^4 + 25*T^3 + 692*T^2 - 1028*T - 904
$71$
\( T^{5} + 12 T^{4} - 69 T^{3} + \cdots + 576 \)
T^5 + 12*T^4 - 69*T^3 - 444*T^2 - 288*T + 576
$73$
\( T^{5} - 4 T^{4} - 83 T^{3} + \cdots - 3832 \)
T^5 - 4*T^4 - 83*T^3 + 254*T^2 + 1552*T - 3832
$79$
\( T^{5} - 28 T^{4} + 184 T^{3} + \cdots + 8352 \)
T^5 - 28*T^4 + 184*T^3 + 528*T^2 - 5616*T + 8352
$83$
\( T^{5} - 18 T^{4} + 3 T^{3} + \cdots + 9000 \)
T^5 - 18*T^4 + 3*T^3 + 1230*T^2 - 6300*T + 9000
$89$
\( T^{5} - 228 T^{3} + 1284 T^{2} + \cdots - 3753 \)
T^5 - 228*T^3 + 1284*T^2 - 711*T - 3753
$97$
\( T^{5} - 4 T^{4} - 80 T^{3} + 226 T^{2} + \cdots + 127 \)
T^5 - 4*T^4 - 80*T^3 + 226*T^2 + 1157*T + 127
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