[N,k,chi] = [1560,4,Mod(1,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1560.1");
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
\(2\)
\(1\)
\(3\)
\(-1\)
\(5\)
\(1\)
\(13\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{7}^{4} - 15T_{7}^{3} - 762T_{7}^{2} + 6048T_{7} + 101088 \)
T7^4 - 15*T7^3 - 762*T7^2 + 6048*T7 + 101088
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1560))\).
$p$
$F_p(T)$
$2$
\( T^{4} \)
T^4
$3$
\( (T - 3)^{4} \)
(T - 3)^4
$5$
\( (T + 5)^{4} \)
(T + 5)^4
$7$
\( T^{4} - 15 T^{3} - 762 T^{2} + \cdots + 101088 \)
T^4 - 15*T^3 - 762*T^2 + 6048*T + 101088
$11$
\( T^{4} + 7 T^{3} - 4536 T^{2} + \cdots + 1081600 \)
T^4 + 7*T^3 - 4536*T^2 - 82160*T + 1081600
$13$
\( (T - 13)^{4} \)
(T - 13)^4
$17$
\( T^{4} + 73 T^{3} - 2304 T^{2} + \cdots + 237376 \)
T^4 + 73*T^3 - 2304*T^2 - 15020*T + 237376
$19$
\( T^{4} - 68 T^{3} - 7020 T^{2} + \cdots + 3677440 \)
T^4 - 68*T^3 - 7020*T^2 + 270784*T + 3677440
$23$
\( T^{4} + 49 T^{3} - 3402 T^{2} + \cdots + 230080 \)
T^4 + 49*T^3 - 3402*T^2 + 19648*T + 230080
$29$
\( T^{4} + 66 T^{3} - 12228 T^{2} + \cdots - 1489536 \)
T^4 + 66*T^3 - 12228*T^2 - 642888*T - 1489536
$31$
\( T^{4} - 230 T^{3} + \cdots + 26955136 \)
T^4 - 230*T^3 - 9336*T^2 + 743584*T + 26955136
$37$
\( T^{4} - 303 T^{3} + \cdots - 62816472 \)
T^4 - 303*T^3 + 17154*T^2 + 1122012*T - 62816472
$41$
\( T^{4} - 155 T^{3} + \cdots + 289265992 \)
T^4 - 155*T^3 - 90918*T^2 + 10034380*T + 289265992
$43$
\( T^{4} - 336 T^{3} + \cdots - 30613248 \)
T^4 - 336*T^3 + 6240*T^2 + 2292480*T - 30613248
$47$
\( T^{4} - 178 T^{3} + \cdots + 27520000 \)
T^4 - 178*T^3 - 19008*T^2 + 180800*T + 27520000
$53$
\( T^{4} - 349 T^{3} + \cdots + 77826040 \)
T^4 - 349*T^3 - 71298*T^2 + 25424756*T + 77826040
$59$
\( T^{4} + 360 T^{3} + \cdots + 30371328000 \)
T^4 + 360*T^3 - 394512*T^2 - 36241920*T + 30371328000
$61$
\( T^{4} - 223 T^{3} + \cdots + 9467381272 \)
T^4 - 223*T^3 - 338466*T^2 + 67414604*T + 9467381272
$67$
\( T^{4} - 588 T^{3} + \cdots + 5005863936 \)
T^4 - 588*T^3 - 329280*T^2 + 185072256*T + 5005863936
$71$
\( T^{4} + 83 T^{3} + \cdots + 4244171776 \)
T^4 + 83*T^3 - 594864*T^2 - 104482720*T + 4244171776
$73$
\( T^{4} - 754 T^{3} + \cdots - 50664163520 \)
T^4 - 754*T^3 - 938772*T^2 + 586517192*T - 50664163520
$79$
\( T^{4} - 869 T^{3} + \cdots + 239698264576 \)
T^4 - 869*T^3 - 988056*T^2 + 321307840*T + 239698264576
$83$
\( T^{4} + 1044 T^{3} + \cdots - 909439488 \)
T^4 + 1044*T^3 + 34416*T^2 - 16113600*T - 909439488
$89$
\( T^{4} - 1017 T^{3} + \cdots + 6573954600 \)
T^4 - 1017*T^3 - 1156614*T^2 + 735163380*T + 6573954600
$97$
\( T^{4} - 1367 T^{3} + \cdots - 193647346784 \)
T^4 - 1367*T^3 - 1348920*T^2 + 1838238292*T - 193647346784
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