[N,k,chi] = [4100,2,Mod(1,4100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4100, 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("4100.1");
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
\(2\)
\(-1\)
\(5\)
\(-1\)
\(41\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{7} - 3T_{3}^{6} - 9T_{3}^{5} + 23T_{3}^{4} + 21T_{3}^{3} - 30T_{3}^{2} - 27T_{3} - 3 \)
T3^7 - 3*T3^6 - 9*T3^5 + 23*T3^4 + 21*T3^3 - 30*T3^2 - 27*T3 - 3
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4100))\).
$p$
$F_p(T)$
$2$
\( T^{7} \)
T^7
$3$
\( T^{7} - 3 T^{6} - 9 T^{5} + 23 T^{4} + \cdots - 3 \)
T^7 - 3*T^6 - 9*T^5 + 23*T^4 + 21*T^3 - 30*T^2 - 27*T - 3
$5$
\( T^{7} \)
T^7
$7$
\( T^{7} - 23 T^{5} + 5 T^{4} + 100 T^{3} + \cdots - 1 \)
T^7 - 23*T^5 + 5*T^4 + 100*T^3 - 40*T^2 - 15*T - 1
$11$
\( T^{7} + T^{6} - 42 T^{5} - 51 T^{4} + \cdots + 432 \)
T^7 + T^6 - 42*T^5 - 51*T^4 + 453*T^3 + 435*T^2 - 1116*T + 432
$13$
\( T^{7} - 5 T^{6} - 31 T^{5} + \cdots + 1617 \)
T^7 - 5*T^6 - 31*T^5 + 121*T^4 + 245*T^3 - 848*T^2 - 497*T + 1617
$17$
\( T^{7} - 11 T^{6} - 6 T^{5} + 481 T^{4} + \cdots + 108 \)
T^7 - 11*T^6 - 6*T^5 + 481*T^4 - 2087*T^3 + 3099*T^2 - 1104*T + 108
$19$
\( T^{7} + T^{6} - 61 T^{5} + 80 T^{4} + \cdots + 1269 \)
T^7 + T^6 - 61*T^5 + 80*T^4 + 597*T^3 - 1242*T^2 - 297*T + 1269
$23$
\( T^{7} + 4 T^{6} - 111 T^{5} + \cdots - 12447 \)
T^7 + 4*T^6 - 111*T^5 - 468*T^4 + 3222*T^3 + 13122*T^2 - 12150*T - 12447
$29$
\( T^{7} + 5 T^{6} - 33 T^{5} + \cdots - 2673 \)
T^7 + 5*T^6 - 33*T^5 - 139*T^4 + 331*T^3 + 1170*T^2 - 945*T - 2673
$31$
\( T^{7} - 4 T^{6} - 71 T^{5} + \cdots - 7857 \)
T^7 - 4*T^6 - 71*T^5 + 75*T^4 + 1524*T^3 + 1572*T^2 - 5541*T - 7857
$37$
\( T^{7} - 32 T^{6} + 281 T^{5} + \cdots + 16431 \)
T^7 - 32*T^6 + 281*T^5 + 470*T^4 - 14460*T^3 + 28218*T^2 + 80154*T + 16431
$41$
\( (T - 1)^{7} \)
(T - 1)^7
$43$
\( T^{7} - 4 T^{6} - 171 T^{5} + \cdots + 2468 \)
T^7 - 4*T^6 - 171*T^5 + 812*T^4 + 2614*T^3 - 1887*T^2 - 3674*T + 2468
$47$
\( T^{7} - 8 T^{6} - 105 T^{5} + \cdots + 13131 \)
T^7 - 8*T^6 - 105*T^5 + 729*T^4 + 2082*T^3 - 7584*T^2 - 8874*T + 13131
$53$
\( T^{7} - 8 T^{6} - 168 T^{5} + \cdots - 9153 \)
T^7 - 8*T^6 - 168*T^5 + 1036*T^4 + 4009*T^3 - 10119*T^2 - 28050*T - 9153
$59$
\( T^{7} + 16 T^{6} - 138 T^{5} + \cdots - 270621 \)
T^7 + 16*T^6 - 138*T^5 - 2726*T^4 - 578*T^3 + 74757*T^2 + 116802*T - 270621
$61$
\( T^{7} - 10 T^{6} - 171 T^{5} + \cdots - 5747 \)
T^7 - 10*T^6 - 171*T^5 + 1524*T^4 + 4158*T^3 - 20172*T^2 - 32956*T - 5747
$67$
\( T^{7} - 16 T^{6} - 138 T^{5} + \cdots - 1500443 \)
T^7 - 16*T^6 - 138*T^5 + 3432*T^4 - 6459*T^3 - 163281*T^2 + 976556*T - 1500443
$71$
\( T^{7} - 27 T^{6} - 10 T^{5} + \cdots - 55479 \)
T^7 - 27*T^6 - 10*T^5 + 5338*T^4 - 44613*T^3 + 112718*T^2 - 60492*T - 55479
$73$
\( T^{7} - 27 T^{6} + 72 T^{5} + \cdots - 655971 \)
T^7 - 27*T^6 + 72*T^5 + 3136*T^4 - 21417*T^3 - 41424*T^2 + 455874*T - 655971
$79$
\( T^{7} + T^{6} - 298 T^{5} + \cdots - 2704419 \)
T^7 + T^6 - 298*T^5 - 1004*T^4 + 26165*T^3 + 135427*T^2 - 451892*T - 2704419
$83$
\( T^{7} + 4 T^{6} - 36 T^{5} - 179 T^{4} + \cdots - 108 \)
T^7 + 4*T^6 - 36*T^5 - 179*T^4 - 56*T^3 + 339*T^2 + 48*T - 108
$89$
\( T^{7} + 16 T^{6} - 188 T^{5} + \cdots + 979827 \)
T^7 + 16*T^6 - 188*T^5 - 3976*T^4 - 565*T^3 + 233477*T^2 + 991332*T + 979827
$97$
\( T^{7} - 27 T^{6} - 66 T^{5} + \cdots + 167007 \)
T^7 - 27*T^6 - 66*T^5 + 6454*T^4 - 44937*T^3 + 18531*T^2 + 305088*T + 167007
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