[N,k,chi] = [83,2,Mod(1,83)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(83, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("83.1");
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
\(83\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{6} - T_{2}^{5} - 9T_{2}^{4} + 7T_{2}^{3} + 20T_{2}^{2} - 12T_{2} - 8 \)
T2^6 - T2^5 - 9*T2^4 + 7*T2^3 + 20*T2^2 - 12*T2 - 8
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(83))\).
$p$
$F_p(T)$
$2$
\( T^{6} - T^{5} - 9 T^{4} + 7 T^{3} + 20 T^{2} + \cdots - 8 \)
T^6 - T^5 - 9*T^4 + 7*T^3 + 20*T^2 - 12*T - 8
$3$
\( T^{6} - T^{5} - 10 T^{4} + 5 T^{3} + \cdots - 25 \)
T^6 - T^5 - 10*T^4 + 5*T^3 + 30*T^2 - 4*T - 25
$5$
\( T^{6} - 2 T^{5} - 20 T^{4} + 28 T^{3} + \cdots - 160 \)
T^6 - 2*T^5 - 20*T^4 + 28*T^3 + 104*T^2 - 64*T - 160
$7$
\( T^{6} - 3 T^{5} - 22 T^{4} + 55 T^{3} + \cdots - 409 \)
T^6 - 3*T^5 - 22*T^4 + 55*T^3 + 154*T^2 - 228*T - 409
$11$
\( T^{6} + 3 T^{5} - 26 T^{4} - 83 T^{3} + \cdots - 113 \)
T^6 + 3*T^5 - 26*T^4 - 83*T^3 + 66*T^2 + 156*T - 113
$13$
\( T^{6} - 14 T^{5} + 44 T^{4} + \cdots + 992 \)
T^6 - 14*T^5 + 44*T^4 + 108*T^3 - 488*T^2 - 288*T + 992
$17$
\( T^{6} + 5 T^{5} - 20 T^{4} - 77 T^{3} + \cdots - 275 \)
T^6 + 5*T^5 - 20*T^4 - 77*T^3 + 162*T^2 + 188*T - 275
$19$
\( T^{6} + 4 T^{5} - 68 T^{4} + \cdots + 6176 \)
T^6 + 4*T^5 - 68*T^4 - 300*T^3 + 976*T^2 + 5648*T + 6176
$23$
\( T^{6} + 5 T^{5} - 61 T^{4} + \cdots + 10912 \)
T^6 + 5*T^5 - 61*T^4 - 377*T^3 + 608*T^2 + 7024*T + 10912
$29$
\( T^{6} + T^{5} - 88 T^{4} - 181 T^{3} + \cdots - 55 \)
T^6 + T^5 - 88*T^4 - 181*T^3 + 578*T^2 - 192*T - 55
$31$
\( T^{6} - 3 T^{5} - 66 T^{4} - 93 T^{3} + \cdots - 313 \)
T^6 - 3*T^5 - 66*T^4 - 93*T^3 + 390*T^2 + 608*T - 313
$37$
\( T^{6} - 39 T^{5} + 576 T^{4} + \cdots - 91499 \)
T^6 - 39*T^5 + 576*T^4 - 3785*T^3 + 7934*T^2 + 22268*T - 91499
$41$
\( T^{6} + T^{5} - 47 T^{4} - T^{3} + \cdots - 248 \)
T^6 + T^5 - 47*T^4 - T^3 + 482*T^2 - 516*T - 248
$43$
\( T^{6} + 8 T^{5} - 44 T^{4} + \cdots + 6400 \)
T^6 + 8*T^5 - 44*T^4 - 456*T^3 - 192*T^2 + 4224*T + 6400
$47$
\( T^{6} + 12 T^{5} - 96 T^{4} + \cdots + 25952 \)
T^6 + 12*T^5 - 96*T^4 - 1812*T^3 - 6648*T^2 + 992*T + 25952
$53$
\( T^{6} - 14 T^{5} - 64 T^{4} + 1064 T^{3} + \cdots - 64 \)
T^6 - 14*T^5 - 64*T^4 + 1064*T^3 + 448*T^2 - 10048*T - 64
$59$
\( T^{6} + 17 T^{5} + 10 T^{4} + \cdots + 3527 \)
T^6 + 17*T^5 + 10*T^4 - 493*T^3 - 1018*T^2 + 1768*T + 3527
$61$
\( T^{6} + 5 T^{5} - 208 T^{4} + \cdots - 47347 \)
T^6 + 5*T^5 - 208*T^4 - 565*T^3 + 10086*T^2 + 1436*T - 47347
$67$
\( T^{6} - 16 T^{5} - 128 T^{4} + \cdots + 264256 \)
T^6 - 16*T^5 - 128*T^4 + 3240*T^3 - 10464*T^2 - 57376*T + 264256
$71$
\( T^{6} + 26 T^{5} + 168 T^{4} + \cdots + 7232 \)
T^6 + 26*T^5 + 168*T^4 - 216*T^3 - 2688*T^2 + 1344*T + 7232
$73$
\( T^{6} + 6 T^{5} - 268 T^{4} + \cdots - 39136 \)
T^6 + 6*T^5 - 268*T^4 - 1484*T^3 + 17920*T^2 + 94416*T - 39136
$79$
\( T^{6} + 12 T^{5} - 12 T^{4} + \cdots - 160 \)
T^6 + 12*T^5 - 12*T^4 - 268*T^3 + 112*T^2 + 304*T - 160
$83$
\( (T - 1)^{6} \)
(T - 1)^6
$89$
\( T^{6} + 22 T^{5} - 28 T^{4} + \cdots + 144896 \)
T^6 + 22*T^5 - 28*T^4 - 2424*T^3 - 3232*T^2 + 56960*T + 144896
$97$
\( T^{6} - 6 T^{5} - 300 T^{4} + \cdots - 101120 \)
T^6 - 6*T^5 - 300*T^4 + 1176*T^3 + 19296*T^2 + 9984*T - 101120
show more
show less