[N,k,chi] = [1005,2,Mod(1,1005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1005, 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("1005.1");
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
\(3\)
\(-1\)
\(5\)
\(-1\)
\(67\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{4} + 4T_{2}^{3} + 2T_{2}^{2} - 5T_{2} - 3 \)
T2^4 + 4*T2^3 + 2*T2^2 - 5*T2 - 3
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1005))\).
$p$
$F_p(T)$
$2$
\( T^{4} + 4 T^{3} + 2 T^{2} - 5 T - 3 \)
T^4 + 4*T^3 + 2*T^2 - 5*T - 3
$3$
\( (T - 1)^{4} \)
(T - 1)^4
$5$
\( (T - 1)^{4} \)
(T - 1)^4
$7$
\( T^{4} + 9 T^{3} + 22 T^{2} + 2 T - 31 \)
T^4 + 9*T^3 + 22*T^2 + 2*T - 31
$11$
\( T^{4} + 5 T^{3} - 22 T^{2} - 114 T - 19 \)
T^4 + 5*T^3 - 22*T^2 - 114*T - 19
$13$
\( T^{4} + 5 T^{3} - 29 T^{2} - 113 T + 3 \)
T^4 + 5*T^3 - 29*T^2 - 113*T + 3
$17$
\( T^{4} + 14 T^{3} + 60 T^{2} + 93 T + 43 \)
T^4 + 14*T^3 + 60*T^2 + 93*T + 43
$19$
\( T^{4} + 15 T^{3} + 61 T^{2} + \cdots - 301 \)
T^4 + 15*T^3 + 61*T^2 - 5*T - 301
$23$
\( T^{4} + 10 T^{3} - 12 T^{2} + \cdots + 331 \)
T^4 + 10*T^3 - 12*T^2 - 186*T + 331
$29$
\( T^{4} + 17 T^{3} + 57 T^{2} + \cdots - 1559 \)
T^4 + 17*T^3 + 57*T^2 - 315*T - 1559
$31$
\( T^{4} - T^{3} - 114 T^{2} - 92 T + 1869 \)
T^4 - T^3 - 114*T^2 - 92*T + 1869
$37$
\( T^{4} - 4 T^{3} - 58 T^{2} - 76 T + 89 \)
T^4 - 4*T^3 - 58*T^2 - 76*T + 89
$41$
\( T^{4} - T^{3} - 60 T^{2} + 16 T + 147 \)
T^4 - T^3 - 60*T^2 + 16*T + 147
$43$
\( T^{4} + 19 T^{3} + 98 T^{2} + \cdots - 991 \)
T^4 + 19*T^3 + 98*T^2 - 44*T - 991
$47$
\( T^{4} + 7 T^{3} - 87 T^{2} - 157 T + 47 \)
T^4 + 7*T^3 - 87*T^2 - 157*T + 47
$53$
\( T^{4} + 11 T^{3} + 17 T^{2} + \cdots - 267 \)
T^4 + 11*T^3 + 17*T^2 - 109*T - 267
$59$
\( T^{4} + 17 T^{3} - T^{2} - 607 T + 441 \)
T^4 + 17*T^3 - T^2 - 607*T + 441
$61$
\( T^{4} + 11 T^{3} - 75 T^{2} + \cdots + 2437 \)
T^4 + 11*T^3 - 75*T^2 - 561*T + 2437
$67$
\( (T + 1)^{4} \)
(T + 1)^4
$71$
\( T^{4} - 22 T^{3} + 74 T^{2} + \cdots - 4599 \)
T^4 - 22*T^3 + 74*T^2 + 935*T - 4599
$73$
\( T^{4} - 16 T^{3} - 154 T^{2} + \cdots + 11589 \)
T^4 - 16*T^3 - 154*T^2 + 1763*T + 11589
$79$
\( T^{4} - 5 T^{3} - 112 T^{2} + \cdots - 457 \)
T^4 - 5*T^3 - 112*T^2 + 616*T - 457
$83$
\( T^{4} + 12 T^{3} - 66 T^{2} + \cdots + 411 \)
T^4 + 12*T^3 - 66*T^2 - 385*T + 411
$89$
\( T^{4} - 16 T^{3} - 120 T^{2} + \cdots - 4801 \)
T^4 - 16*T^3 - 120*T^2 + 1873*T - 4801
$97$
\( T^{4} + 7 T^{3} - 145 T^{2} + \cdots + 207 \)
T^4 + 7*T^3 - 145*T^2 - 143*T + 207
show more
show less