[N,k,chi] = [1682,4,Mod(1,1682)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1682, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1682.1");
S:= CuspForms(chi, 4);
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
\(2\)
\(-1\)
\(29\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{4} - 4T_{3}^{3} - 94T_{3}^{2} + 331T_{3} + 1314 \)
T3^4 - 4*T3^3 - 94*T3^2 + 331*T3 + 1314
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1682))\).
$p$
$F_p(T)$
$2$
\( (T - 2)^{4} \)
(T - 2)^4
$3$
\( T^{4} - 4 T^{3} - 94 T^{2} + \cdots + 1314 \)
T^4 - 4*T^3 - 94*T^2 + 331*T + 1314
$5$
\( T^{4} + 7 T^{3} - 447 T^{2} + \cdots + 31104 \)
T^4 + 7*T^3 - 447*T^2 - 2556*T + 31104
$7$
\( T^{4} - 39 T^{3} + 131 T^{2} + \cdots + 2916 \)
T^4 - 39*T^3 + 131*T^2 + 1935*T + 2916
$11$
\( T^{4} + 14 T^{3} - 6110 T^{2} + \cdots + 8827542 \)
T^4 + 14*T^3 - 6110*T^2 - 43959*T + 8827542
$13$
\( T^{4} - 98 T^{3} - 105 T^{2} + \cdots - 1829088 \)
T^4 - 98*T^3 - 105*T^2 + 151974*T - 1829088
$17$
\( T^{4} + 86 T^{3} - 5752 T^{2} + \cdots - 2685942 \)
T^4 + 86*T^3 - 5752*T^2 - 311045*T - 2685942
$19$
\( T^{4} - 114 T^{3} - 1454 T^{2} + \cdots - 4967384 \)
T^4 - 114*T^3 - 1454*T^2 + 309525*T - 4967384
$23$
\( T^{4} - 283 T^{3} + \cdots - 25030296 \)
T^4 - 283*T^3 + 19848*T^2 + 190152*T - 25030296
$29$
\( T^{4} \)
T^4
$31$
\( T^{4} + 352 T^{3} + \cdots - 1161813984 \)
T^4 + 352*T^3 - 42850*T^2 - 21253633*T - 1161813984
$37$
\( T^{4} + 354 T^{3} + \cdots - 255228624 \)
T^4 + 354*T^3 + 4535*T^2 - 5031894*T - 255228624
$41$
\( T^{4} - 506 T^{3} + \cdots - 90592182 \)
T^4 - 506*T^3 + 39856*T^2 + 1455747*T - 90592182
$43$
\( T^{4} - 93 T^{3} - 92746 T^{2} + \cdots + 11676096 \)
T^4 - 93*T^3 - 92746*T^2 + 4189740*T + 11676096
$47$
\( T^{4} + 219 T^{3} + \cdots + 1883605644 \)
T^4 + 219*T^3 - 207385*T^2 - 50529567*T + 1883605644
$53$
\( T^{4} + 22 T^{3} + \cdots + 5304263616 \)
T^4 + 22*T^3 - 161204*T^2 + 2409768*T + 5304263616
$59$
\( T^{4} - 1067 T^{3} + \cdots - 246032616 \)
T^4 - 1067*T^3 + 112409*T^2 + 50151602*T - 246032616
$61$
\( T^{4} + 1535 T^{3} + \cdots - 43523877984 \)
T^4 + 1535*T^3 + 620333*T^2 - 37351826*T - 43523877984
$67$
\( T^{4} + 576 T^{3} + \cdots - 866678784 \)
T^4 + 576*T^3 - 338688*T^2 - 73462208*T - 866678784
$71$
\( T^{4} + 601 T^{3} + \cdots - 19289176992 \)
T^4 + 601*T^3 - 907682*T^2 - 609882600*T - 19289176992
$73$
\( T^{4} - 1011 T^{3} + \cdots - 4444444536 \)
T^4 - 1011*T^3 + 21432*T^2 + 51311512*T - 4444444536
$79$
\( T^{4} - 1026 T^{3} + \cdots + 152742025204 \)
T^4 - 1026*T^3 - 585872*T^2 + 378510741*T + 152742025204
$83$
\( T^{4} + 111 T^{3} + \cdots + 17589089088 \)
T^4 + 111*T^3 - 1031805*T^2 + 308611917*T + 17589089088
$89$
\( T^{4} - 2406 T^{3} + \cdots - 60143265909 \)
T^4 - 2406*T^3 + 1601276*T^2 - 144902226*T - 60143265909
$97$
\( T^{4} + 145 T^{3} + \cdots + 4303874709 \)
T^4 + 145*T^3 - 732660*T^2 + 30617613*T + 4303874709
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