[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
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
\(2\)
\(-1\)
\(251\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{5} - T_{3}^{4} - 7T_{3}^{3} + 4T_{3}^{2} + 6T_{3} + 1 \)
T3^5 - T3^4 - 7*T3^3 + 4*T3^2 + 6*T3 + 1
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4016))\).
$p$
$F_p(T)$
$2$
\( T^{5} \)
T^5
$3$
\( T^{5} - T^{4} - 7 T^{3} + 4 T^{2} + 6 T + 1 \)
T^5 - T^4 - 7*T^3 + 4*T^2 + 6*T + 1
$5$
\( T^{5} + 6 T^{4} + 6 T^{3} - 18 T^{2} + \cdots + 7 \)
T^5 + 6*T^4 + 6*T^3 - 18*T^2 - 25*T + 7
$7$
\( T^{5} - T^{4} - 19 T^{3} + 18 T^{2} + \cdots - 73 \)
T^5 - T^4 - 19*T^3 + 18*T^2 + 78*T - 73
$11$
\( T^{5} - 4 T^{4} - 29 T^{3} + 76 T^{2} + \cdots + 64 \)
T^5 - 4*T^4 - 29*T^3 + 76*T^2 + 160*T + 64
$13$
\( T^{5} + 7 T^{4} - 7 T^{3} - 100 T^{2} + \cdots + 373 \)
T^5 + 7*T^4 - 7*T^3 - 100*T^2 - 6*T + 373
$17$
\( T^{5} + 8 T^{4} - 22 T^{3} - 242 T^{2} + \cdots - 313 \)
T^5 + 8*T^4 - 22*T^3 - 242*T^2 - 501*T - 313
$19$
\( T^{5} + 3 T^{4} - 13 T^{3} + 2 T^{2} + \cdots - 8 \)
T^5 + 3*T^4 - 13*T^3 + 2*T^2 + 16*T - 8
$23$
\( T^{5} - 17 T^{4} + 79 T^{3} + \cdots + 1999 \)
T^5 - 17*T^4 + 79*T^3 + 66*T^2 - 1196*T + 1999
$29$
\( T^{5} + 15 T^{4} + 69 T^{3} + \cdots - 536 \)
T^5 + 15*T^4 + 69*T^3 + 48*T^2 - 340*T - 536
$31$
\( T^{5} - T^{4} - 80 T^{3} - 15 T^{2} + \cdots + 1796 \)
T^5 - T^4 - 80*T^3 - 15*T^2 + 1588*T + 1796
$37$
\( T^{5} + 5 T^{4} - 131 T^{3} + \cdots + 968 \)
T^5 + 5*T^4 - 131*T^3 - 810*T^2 - 704*T + 968
$41$
\( T^{5} + 12 T^{4} - 44 T^{3} + \cdots + 8119 \)
T^5 + 12*T^4 - 44*T^3 - 756*T^2 - 245*T + 8119
$43$
\( T^{5} + T^{4} - 43 T^{3} + 114 T^{2} + \cdots + 8 \)
T^5 + T^4 - 43*T^3 + 114*T^2 - 88*T + 8
$47$
\( T^{5} - 19 T^{4} + 97 T^{3} + \cdots - 472 \)
T^5 - 19*T^4 + 97*T^3 + 50*T^2 - 916*T - 472
$53$
\( T^{5} + 34 T^{4} + 360 T^{3} + \cdots - 3424 \)
T^5 + 34*T^4 + 360*T^3 + 864*T^2 - 3744*T - 3424
$59$
\( T^{5} - 10 T^{4} - 36 T^{3} + \cdots - 512 \)
T^5 - 10*T^4 - 36*T^3 + 392*T^2 - 448*T - 512
$61$
\( T^{5} - 171 T^{3} + 54 T^{2} + \cdots - 1944 \)
T^5 - 171*T^3 + 54*T^2 + 2268*T - 1944
$67$
\( T^{5} - 11 T^{4} - 7 T^{3} + \cdots - 1331 \)
T^5 - 11*T^4 - 7*T^3 + 264*T^2 - 1331
$71$
\( T^{5} - T^{4} - 231 T^{3} + \cdots - 33224 \)
T^5 - T^4 - 231*T^3 + 294*T^2 + 11968*T - 33224
$73$
\( T^{5} - 3 T^{4} - 82 T^{3} - 77 T^{2} + \cdots - 208 \)
T^5 - 3*T^4 - 82*T^3 - 77*T^2 + 476*T - 208
$79$
\( T^{5} + 35 T^{4} + 453 T^{3} + \cdots + 6209 \)
T^5 + 35*T^4 + 453*T^3 + 2670*T^2 + 6968*T + 6209
$83$
\( T^{5} + 3 T^{4} - 289 T^{3} + \cdots + 48832 \)
T^5 + 3*T^4 - 289*T^3 - 676*T^2 + 19136*T + 48832
$89$
\( T^{5} - 15 T^{4} + 5 T^{3} + 514 T^{2} + \cdots + 77 \)
T^5 - 15*T^4 + 5*T^3 + 514*T^2 - 674*T + 77
$97$
\( T^{5} + 2 T^{4} - 353 T^{3} + \cdots + 109064 \)
T^5 + 2*T^4 - 353*T^3 - 1094*T^2 + 27328*T + 109064
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