[N,k,chi] = [1335,2,Mod(1,1335)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1335, 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("1335.1");
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
\(3\)
\(1\)
\(5\)
\(1\)
\(89\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{6} + 4T_{2}^{5} - 2T_{2}^{4} - 21T_{2}^{3} - 13T_{2}^{2} + 11T_{2} + 4 \)
T2^6 + 4*T2^5 - 2*T2^4 - 21*T2^3 - 13*T2^2 + 11*T2 + 4
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1335))\).
$p$
$F_p(T)$
$2$
\( T^{6} + 4 T^{5} - 2 T^{4} - 21 T^{3} + \cdots + 4 \)
T^6 + 4*T^5 - 2*T^4 - 21*T^3 - 13*T^2 + 11*T + 4
$3$
\( (T + 1)^{6} \)
(T + 1)^6
$5$
\( (T + 1)^{6} \)
(T + 1)^6
$7$
\( T^{6} - T^{5} - 20 T^{4} + 7 T^{3} + \cdots - 128 \)
T^6 - T^5 - 20*T^4 + 7*T^3 + 96*T^2 - 16*T - 128
$11$
\( T^{6} \)
T^6
$13$
\( T^{6} + 3 T^{5} - 20 T^{4} - 17 T^{3} + \cdots - 32 \)
T^6 + 3*T^5 - 20*T^4 - 17*T^3 + 70*T^2 + 32*T - 32
$17$
\( T^{6} + 13 T^{5} + 22 T^{4} + \cdots - 128 \)
T^6 + 13*T^5 + 22*T^4 - 263*T^3 - 1052*T^2 - 1100*T - 128
$19$
\( (T - 2)^{6} \)
(T - 2)^6
$23$
\( T^{6} + 19 T^{5} + 114 T^{4} + \cdots - 2048 \)
T^6 + 19*T^5 + 114*T^4 + 136*T^3 - 872*T^2 - 2688*T - 2048
$29$
\( T^{6} - 55 T^{4} + 157 T^{3} + \cdots + 652 \)
T^6 - 55*T^4 + 157*T^3 + 171*T^2 - 880*T + 652
$31$
\( T^{6} - 10 T^{5} - 40 T^{4} + \cdots - 3904 \)
T^6 - 10*T^5 - 40*T^4 + 504*T^3 + 32*T^2 - 3776*T - 3904
$37$
\( T^{6} + T^{5} - 48 T^{4} - 79 T^{3} + \cdots - 32 \)
T^6 + T^5 - 48*T^4 - 79*T^3 + 254*T^2 + 96*T - 32
$41$
\( T^{6} + 4 T^{5} - 117 T^{4} + \cdots - 4964 \)
T^6 + 4*T^5 - 117*T^4 - 23*T^3 + 2143*T^2 - 1920*T - 4964
$43$
\( T^{6} + 7 T^{5} - 72 T^{4} + \cdots + 1024 \)
T^6 + 7*T^5 - 72*T^4 - 265*T^3 + 836*T^2 + 2496*T + 1024
$47$
\( T^{6} + 15 T^{5} + 26 T^{4} + \cdots + 512 \)
T^6 + 15*T^5 + 26*T^4 - 323*T^3 - 560*T^2 + 1920*T + 512
$53$
\( T^{6} + 27 T^{5} + 174 T^{4} + \cdots - 34376 \)
T^6 + 27*T^5 + 174*T^4 - 927*T^3 - 13222*T^2 - 39060*T - 34376
$59$
\( T^{6} + 4 T^{5} - 39 T^{4} - 147 T^{3} + \cdots - 4 \)
T^6 + 4*T^5 - 39*T^4 - 147*T^3 + 279*T^2 + 832*T - 4
$61$
\( T^{6} - 8 T^{5} - 92 T^{4} + \cdots - 1024 \)
T^6 - 8*T^5 - 92*T^4 + 144*T^3 + 1088*T^2 - 1536*T - 1024
$67$
\( T^{6} + 11 T^{5} - 204 T^{4} + \cdots + 53888 \)
T^6 + 11*T^5 - 204*T^4 - 1684*T^3 + 10136*T^2 + 52160*T + 53888
$71$
\( T^{6} + 16 T^{5} - 68 T^{4} + \cdots + 22016 \)
T^6 + 16*T^5 - 68*T^4 - 2024*T^3 - 6944*T^2 + 6784*T + 22016
$73$
\( T^{6} - T^{5} - 442 T^{4} + \cdots - 2343136 \)
T^6 - T^5 - 442*T^4 + 212*T^3 + 59136*T^2 - 18208*T - 2343136
$79$
\( T^{6} - 121 T^{4} + 39 T^{3} + \cdots - 10048 \)
T^6 - 121*T^4 + 39*T^3 + 3799*T^2 - 2576*T - 10048
$83$
\( T^{6} + 17 T^{5} + 52 T^{4} + \cdots + 512 \)
T^6 + 17*T^5 + 52*T^4 - 132*T^3 - 488*T^2 + 256*T + 512
$89$
\( (T + 1)^{6} \)
(T + 1)^6
$97$
\( T^{6} + 29 T^{5} + 134 T^{4} + \cdots - 30112 \)
T^6 + 29*T^5 + 134*T^4 - 1784*T^3 - 7232*T^2 + 43792*T - 30112
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