[N,k,chi] = [9660,2,Mod(1,9660)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9660, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("9660.1");
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
\(2\)
\(-1\)
\(3\)
\(1\)
\(5\)
\(1\)
\(7\)
\(1\)
\(23\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{11}^{7} - 4T_{11}^{6} - 48T_{11}^{5} + 161T_{11}^{4} + 718T_{11}^{3} - 2086T_{11}^{2} - 3370T_{11} + 8972 \)
T11^7 - 4*T11^6 - 48*T11^5 + 161*T11^4 + 718*T11^3 - 2086*T11^2 - 3370*T11 + 8972
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(9660))\).
$p$
$F_p(T)$
$2$
\( T^{7} \)
T^7
$3$
\( (T + 1)^{7} \)
(T + 1)^7
$5$
\( (T + 1)^{7} \)
(T + 1)^7
$7$
\( (T + 1)^{7} \)
(T + 1)^7
$11$
\( T^{7} - 4 T^{6} - 48 T^{5} + \cdots + 8972 \)
T^7 - 4*T^6 - 48*T^5 + 161*T^4 + 718*T^3 - 2086*T^2 - 3370*T + 8972
$13$
\( T^{7} + 5 T^{6} - 49 T^{5} - 292 T^{4} + \cdots + 864 \)
T^7 + 5*T^6 - 49*T^5 - 292*T^4 + 276*T^3 + 3210*T^2 + 3456*T + 864
$17$
\( T^{7} + 5 T^{6} - 77 T^{5} + \cdots + 2528 \)
T^7 + 5*T^6 - 77*T^5 - 250*T^4 + 1896*T^3 + 1952*T^2 - 12816*T + 2528
$19$
\( T^{7} + 6 T^{6} - 56 T^{5} - 325 T^{4} + \cdots + 216 \)
T^7 + 6*T^6 - 56*T^5 - 325*T^4 + 706*T^3 + 3308*T^2 - 3132*T + 216
$23$
\( (T - 1)^{7} \)
(T - 1)^7
$29$
\( T^{7} - 6 T^{6} - 128 T^{5} + \cdots + 30528 \)
T^7 - 6*T^6 - 128*T^5 + 668*T^4 + 3752*T^3 - 19840*T^2 + 6624*T + 30528
$31$
\( T^{7} + 2 T^{6} - 114 T^{5} + \cdots + 14592 \)
T^7 + 2*T^6 - 114*T^5 - 10*T^4 + 3604*T^3 - 5912*T^2 - 10416*T + 14592
$37$
\( T^{7} - 13 T^{6} - 143 T^{5} + \cdots - 939384 \)
T^7 - 13*T^6 - 143*T^5 + 2586*T^4 - 2026*T^3 - 118986*T^2 + 624312*T - 939384
$41$
\( T^{7} + 6 T^{6} - 184 T^{5} + \cdots - 715632 \)
T^7 + 6*T^6 - 184*T^5 - 1107*T^4 + 9168*T^3 + 51616*T^2 - 134256*T - 715632
$43$
\( T^{7} + 5 T^{6} - 69 T^{5} - 548 T^{4} + \cdots - 64 \)
T^7 + 5*T^6 - 69*T^5 - 548*T^4 - 1240*T^3 - 1168*T^2 - 464*T - 64
$47$
\( T^{7} + 5 T^{6} - 200 T^{5} + \cdots + 6912 \)
T^7 + 5*T^6 - 200*T^5 - 300*T^4 + 10008*T^3 - 32384*T^2 + 27360*T + 6912
$53$
\( T^{7} + 3 T^{6} - 180 T^{5} + \cdots + 69984 \)
T^7 + 3*T^6 - 180*T^5 - 432*T^4 + 8910*T^3 + 13608*T^2 - 87480*T + 69984
$59$
\( T^{7} - 18 T^{6} - 32 T^{5} + \cdots + 17904 \)
T^7 - 18*T^6 - 32*T^5 + 1423*T^4 - 2334*T^3 - 11972*T^2 + 11754*T + 17904
$61$
\( T^{7} - 8 T^{6} - 48 T^{5} + \cdots - 3256 \)
T^7 - 8*T^6 - 48*T^5 + 659*T^4 - 2062*T^3 + 1064*T^2 + 3764*T - 3256
$67$
\( T^{7} - 3 T^{6} - 185 T^{5} + \cdots - 185344 \)
T^7 - 3*T^6 - 185*T^5 - 94*T^4 + 8648*T^3 + 14080*T^2 - 108032*T - 185344
$71$
\( T^{7} - 12 T^{6} - 136 T^{5} + \cdots - 349952 \)
T^7 - 12*T^6 - 136*T^5 + 2356*T^4 - 5376*T^3 - 49504*T^2 + 262880*T - 349952
$73$
\( T^{7} + 5 T^{6} - 285 T^{5} + \cdots - 4147632 \)
T^7 + 5*T^6 - 285*T^5 - 1464*T^4 + 26208*T^3 + 136778*T^2 - 781020*T - 4147632
$79$
\( T^{7} - 12 T^{6} - 20 T^{5} + \cdots + 10368 \)
T^7 - 12*T^6 - 20*T^5 + 422*T^4 + 260*T^3 - 4504*T^2 - 3024*T + 10368
$83$
\( T^{7} + 11 T^{6} - 393 T^{5} + \cdots - 46336 \)
T^7 + 11*T^6 - 393*T^5 - 4760*T^4 + 28220*T^3 + 360716*T^2 - 64208*T - 46336
$89$
\( T^{7} - 16 T^{6} + 20 T^{5} + \cdots - 16384 \)
T^7 - 16*T^6 + 20*T^5 + 636*T^4 - 2024*T^3 - 4032*T^2 + 19456*T - 16384
$97$
\( T^{7} - 2 T^{6} - 460 T^{5} + \cdots - 366336 \)
T^7 - 2*T^6 - 460*T^5 + 796*T^4 + 51936*T^3 - 30336*T^2 - 472608*T - 366336
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