[N,k,chi] = [1380,4,Mod(1,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.1");
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
\(2\)
\(-1\)
\(3\)
\(-1\)
\(5\)
\(1\)
\(23\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{7}^{5} + 5T_{7}^{4} - 755T_{7}^{3} + 3239T_{7}^{2} + 59806T_{7} - 228832 \)
T7^5 + 5*T7^4 - 755*T7^3 + 3239*T7^2 + 59806*T7 - 228832
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1380))\).
$p$
$F_p(T)$
$2$
\( T^{5} \)
T^5
$3$
\( (T - 3)^{5} \)
(T - 3)^5
$5$
\( (T + 5)^{5} \)
(T + 5)^5
$7$
\( T^{5} + 5 T^{4} - 755 T^{3} + \cdots - 228832 \)
T^5 + 5*T^4 - 755*T^3 + 3239*T^2 + 59806*T - 228832
$11$
\( T^{5} + 18 T^{4} - 1218 T^{3} + \cdots + 1134912 \)
T^5 + 18*T^4 - 1218*T^3 - 15932*T^2 + 325632*T + 1134912
$13$
\( T^{5} - 8 T^{4} - 7138 T^{3} + \cdots - 26116032 \)
T^5 - 8*T^4 - 7138*T^3 - 3472*T^2 + 3512760*T - 26116032
$17$
\( T^{5} + 31 T^{4} - 9533 T^{3} + \cdots + 69622200 \)
T^5 + 31*T^4 - 9533*T^3 + 66651*T^2 + 7934610*T + 69622200
$19$
\( T^{5} + 84 T^{4} + \cdots + 532012032 \)
T^5 + 84*T^4 - 4830*T^3 - 425864*T^2 + 5669952*T + 532012032
$23$
\( (T - 23)^{5} \)
(T - 23)^5
$29$
\( T^{5} + 65 T^{4} + \cdots + 11943825132 \)
T^5 + 65*T^4 - 43135*T^3 - 2157755*T^2 + 240551076*T + 11943825132
$31$
\( T^{5} + 81 T^{4} + \cdots + 2185574592 \)
T^5 + 81*T^4 - 57837*T^3 - 1938869*T^2 + 67406640*T + 2185574592
$37$
\( T^{5} + 373 T^{4} + \cdots + 27197717200 \)
T^5 + 373*T^4 - 1547*T^3 - 8154017*T^2 + 65384110*T + 27197717200
$41$
\( T^{5} + 339 T^{4} + \cdots - 177333137460 \)
T^5 + 339*T^4 - 35463*T^3 - 27908973*T^2 - 3932747928*T - 177333137460
$43$
\( T^{5} + 796 T^{4} + \cdots - 4086918988800 \)
T^5 + 796*T^4 + 24468*T^3 - 137705312*T^2 - 43745272256*T - 4086918988800
$47$
\( T^{5} + 382 T^{4} + \cdots + 8652627173376 \)
T^5 + 382*T^4 - 417342*T^3 - 134126772*T^2 + 37195632000*T + 8652627173376
$53$
\( T^{5} + 341 T^{4} + \cdots + 991870895052 \)
T^5 + 341*T^4 - 361215*T^3 - 174794607*T^2 - 13232810916*T + 991870895052
$59$
\( T^{5} - 457 T^{4} + \cdots + 640764426672 \)
T^5 - 457*T^4 - 310167*T^3 - 6326421*T^2 + 9144072792*T + 640764426672
$61$
\( T^{5} + 780 T^{4} + \cdots + 1681676978400 \)
T^5 + 780*T^4 - 246038*T^3 - 163452960*T^2 + 36205175224*T + 1681676978400
$67$
\( T^{5} + 299 T^{4} + \cdots - 55666166592992 \)
T^5 + 299*T^4 - 1025861*T^3 - 49583843*T^2 + 290450346284*T - 55666166592992
$71$
\( T^{5} - 11 T^{4} + \cdots + 4782857500224 \)
T^5 - 11*T^4 - 519103*T^3 + 6752525*T^2 + 43507839540*T + 4782857500224
$73$
\( T^{5} + 1092 T^{4} + \cdots + 29125225312416 \)
T^5 + 1092*T^4 - 627810*T^3 - 903196808*T^2 - 155291601384*T + 29125225312416
$79$
\( T^{5} + 1290 T^{4} + \cdots + 6401513062400 \)
T^5 + 1290*T^4 - 423616*T^3 - 794546144*T^2 - 136357854720*T + 6401513062400
$83$
\( T^{5} + 659 T^{4} + \cdots - 3169995431040 \)
T^5 + 659*T^4 - 409177*T^3 - 144509597*T^2 + 65791621722*T - 3169995431040
$89$
\( T^{5} + \cdots + 182366718082560 \)
T^5 + 1574*T^4 - 670832*T^3 - 1482851472*T^2 - 138324829632*T + 182366718082560
$97$
\( T^{5} + 1462 T^{4} + \cdots + 4996197291840 \)
T^5 + 1462*T^4 - 340732*T^3 - 221398696*T^2 + 6074246112*T + 4996197291840
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