[N,k,chi] = [1336,2,Mod(1,1336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1336, 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("1336.1");
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
\(2\)
\(1\)
\(167\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{7} + 6T_{3}^{6} + 6T_{3}^{5} - 20T_{3}^{4} - 30T_{3}^{3} + 17T_{3}^{2} + 26T_{3} + 1 \)
T3^7 + 6*T3^6 + 6*T3^5 - 20*T3^4 - 30*T3^3 + 17*T3^2 + 26*T3 + 1
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1336))\).
$p$
$F_p(T)$
$2$
\( T^{7} \)
T^7
$3$
\( T^{7} + 6 T^{6} + 6 T^{5} - 20 T^{4} + \cdots + 1 \)
T^7 + 6*T^6 + 6*T^5 - 20*T^4 - 30*T^3 + 17*T^2 + 26*T + 1
$5$
\( T^{7} - 19 T^{5} - 6 T^{4} + 92 T^{3} + \cdots + 32 \)
T^7 - 19*T^5 - 6*T^4 + 92*T^3 + 16*T^2 - 112*T + 32
$7$
\( T^{7} + T^{6} - 17 T^{5} - 8 T^{4} + \cdots + 131 \)
T^7 + T^6 - 17*T^5 - 8*T^4 + 95*T^3 - 16*T^2 - 183*T + 131
$11$
\( T^{7} + 6 T^{6} - 20 T^{5} - 116 T^{4} + \cdots + 41 \)
T^7 + 6*T^6 - 20*T^5 - 116*T^4 + 36*T^3 + 287*T^2 - 230*T + 41
$13$
\( T^{7} + 2 T^{6} - 37 T^{5} - 78 T^{4} + \cdots - 800 \)
T^7 + 2*T^6 - 37*T^5 - 78*T^4 + 268*T^3 + 576*T^2 - 336*T - 800
$17$
\( T^{7} + 9 T^{6} + 3 T^{5} - 120 T^{4} + \cdots - 32 \)
T^7 + 9*T^6 + 3*T^5 - 120*T^4 - 108*T^3 + 368*T^2 - 128*T - 32
$19$
\( T^{7} + 3 T^{6} - 81 T^{5} + \cdots - 17659 \)
T^7 + 3*T^6 - 81*T^5 - 274*T^4 + 1317*T^3 + 4258*T^2 - 6193*T - 17659
$23$
\( T^{7} + 10 T^{6} - 5 T^{5} + \cdots + 4768 \)
T^7 + 10*T^6 - 5*T^5 - 310*T^4 - 724*T^3 + 1424*T^2 + 6064*T + 4768
$29$
\( T^{7} + 5 T^{6} - 77 T^{5} - 288 T^{4} + \cdots - 25 \)
T^7 + 5*T^6 - 77*T^5 - 288*T^4 + 1323*T^3 + 1536*T^2 - 215*T - 25
$31$
\( T^{7} + 21 T^{6} + 99 T^{5} + \cdots + 1447 \)
T^7 + 21*T^6 + 99*T^5 - 366*T^4 - 2365*T^3 + 2538*T^2 + 7341*T + 1447
$37$
\( T^{7} - 19 T^{6} + 101 T^{5} + \cdots - 1024 \)
T^7 - 19*T^6 + 101*T^5 - 68*T^4 - 576*T^3 + 704*T^2 + 768*T - 1024
$41$
\( T^{7} + 22 T^{6} - 17 T^{5} + \cdots + 1855520 \)
T^7 + 22*T^6 - 17*T^5 - 3334*T^4 - 17884*T^3 + 93640*T^2 + 946464*T + 1855520
$43$
\( T^{7} + 19 T^{6} + 29 T^{5} + \cdots - 20000 \)
T^7 + 19*T^6 + 29*T^5 - 1124*T^4 - 4900*T^3 + 5400*T^2 + 26000*T - 20000
$47$
\( T^{7} + 13 T^{6} - 150 T^{5} + \cdots + 383908 \)
T^7 + 13*T^6 - 150*T^5 - 1655*T^4 + 9451*T^3 + 45737*T^2 - 301250*T + 383908
$53$
\( T^{7} - 5 T^{6} - 79 T^{5} + \cdots - 2656 \)
T^7 - 5*T^6 - 79*T^5 + 232*T^4 + 1776*T^3 - 1016*T^2 - 6240*T - 2656
$59$
\( T^{7} + 18 T^{6} + 5 T^{5} + \cdots + 8288 \)
T^7 + 18*T^6 + 5*T^5 - 1004*T^4 - 1628*T^3 + 11232*T^2 + 26368*T + 8288
$61$
\( T^{7} - 26 T^{6} + 110 T^{5} + \cdots + 453613 \)
T^7 - 26*T^6 + 110*T^5 + 2822*T^4 - 39420*T^3 + 207241*T^2 - 497616*T + 453613
$67$
\( T^{7} + 27 T^{6} + 117 T^{5} + \cdots + 459232 \)
T^7 + 27*T^6 + 117*T^5 - 2086*T^4 - 16364*T^3 + 24656*T^2 + 373744*T + 459232
$71$
\( T^{7} + 46 T^{6} + 860 T^{5} + \cdots + 137728 \)
T^7 + 46*T^6 + 860*T^5 + 8408*T^4 + 46080*T^3 + 140704*T^2 + 220800*T + 137728
$73$
\( T^{7} + 25 T^{6} - 43 T^{5} + \cdots - 124640 \)
T^7 + 25*T^6 - 43*T^5 - 5282*T^4 - 40576*T^3 - 42168*T^2 + 269232*T - 124640
$79$
\( T^{7} + 22 T^{6} - 93 T^{5} + \cdots - 404960 \)
T^7 + 22*T^6 - 93*T^5 - 3218*T^4 + 2476*T^3 + 90056*T^2 - 42176*T - 404960
$83$
\( T^{7} - T^{6} - 237 T^{5} + \cdots + 68768 \)
T^7 - T^6 - 237*T^5 + 638*T^4 + 13256*T^3 - 45848*T^2 - 43728*T + 68768
$89$
\( T^{7} + 3 T^{6} - 602 T^{5} + \cdots + 7516100 \)
T^7 + 3*T^6 - 602*T^5 - 1467*T^4 + 104261*T^3 + 159655*T^2 - 4116218*T + 7516100
$97$
\( T^{7} - 11 T^{6} - 162 T^{5} + \cdots + 59188 \)
T^7 - 11*T^6 - 162*T^5 + 811*T^4 + 6893*T^3 - 12171*T^2 - 69290*T + 59188
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