[N,k,chi] = [588,4,Mod(1,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("588.1");
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
\(2\)
\(-1\)
\(3\)
\(1\)
\(7\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{4} - 412T_{5}^{2} + 576T_{5} + 27748 \)
T5^4 - 412*T5^2 + 576*T5 + 27748
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(588))\).
$p$
$F_p(T)$
$2$
\( T^{4} \)
T^4
$3$
\( (T + 3)^{4} \)
(T + 3)^4
$5$
\( T^{4} - 412 T^{2} + 576 T + 27748 \)
T^4 - 412*T^2 + 576*T + 27748
$7$
\( T^{4} \)
T^4
$11$
\( T^{4} - 4136 T^{2} + 82944 T + 733072 \)
T^4 - 4136*T^2 + 82944*T + 733072
$13$
\( T^{4} - 7092 T^{2} + \cdots + 10008036 \)
T^4 - 7092*T^2 + 31104*T + 10008036
$17$
\( T^{4} + 48 T^{3} - 9772 T^{2} + \cdots - 4865084 \)
T^4 + 48*T^3 - 9772*T^2 - 590496*T - 4865084
$19$
\( T^{4} + 192 T^{3} + \cdots - 41971136 \)
T^4 + 192*T^3 - 3280*T^2 - 1549824*T - 41971136
$23$
\( T^{4} - 192 T^{3} + \cdots - 40554608 \)
T^4 - 192*T^3 + 3928*T^2 + 908544*T - 40554608
$29$
\( T^{4} - 96 T^{3} - 11696 T^{2} + \cdots + 38719552 \)
T^4 - 96*T^3 - 11696*T^2 + 648960*T + 38719552
$31$
\( T^{4} + 48 T^{3} + \cdots - 189895104 \)
T^4 + 48*T^3 - 43632*T^2 - 5705856*T - 189895104
$37$
\( T^{4} - 256 T^{3} + \cdots - 1479272192 \)
T^4 - 256*T^3 - 135840*T^2 + 41160704*T - 1479272192
$41$
\( T^{4} + 1008 T^{3} + \cdots + 1611829828 \)
T^4 + 1008*T^3 + 334100*T^2 + 41616864*T + 1611829828
$43$
\( T^{4} + 112 T^{3} + \cdots - 789373952 \)
T^4 + 112*T^3 - 71040*T^2 - 14991872*T - 789373952
$47$
\( T^{4} + 864 T^{3} + \cdots - 1168478144 \)
T^4 + 864*T^3 + 226928*T^2 + 13356288*T - 1168478144
$53$
\( T^{4} + 648 T^{3} + \cdots - 20504773616 \)
T^4 + 648*T^3 - 208616*T^2 - 174760416*T - 20504773616
$59$
\( T^{4} + 336 T^{3} + \cdots + 18986185792 \)
T^4 + 336*T^3 - 287152*T^2 - 47665536*T + 18986185792
$61$
\( T^{4} + 960 T^{3} + \cdots - 106656271196 \)
T^4 + 960*T^3 - 330196*T^2 - 499716480*T - 106656271196
$67$
\( T^{4} - 720 T^{3} + \cdots + 14336621568 \)
T^4 - 720*T^3 - 669312*T^2 + 330683904*T + 14336621568
$71$
\( T^{4} + 1344 T^{3} + \cdots - 17989567344 \)
T^4 + 1344*T^3 + 460440*T^2 - 15945984*T - 17989567344
$73$
\( T^{4} + 672 T^{3} + \cdots - 90986816444 \)
T^4 + 672*T^3 - 467428*T^2 - 459082560*T - 90986816444
$79$
\( T^{4} + 1984 T^{3} + \cdots - 1013049875456 \)
T^4 + 1984*T^3 - 246720*T^2 - 2268354560*T - 1013049875456
$83$
\( T^{4} + 3120 T^{3} + \cdots + 74256064768 \)
T^4 + 3120*T^3 + 3243872*T^2 + 1203548928*T + 74256064768
$89$
\( T^{4} + 2160 T^{3} + \cdots - 311467391228 \)
T^4 + 2160*T^3 + 523124*T^2 - 994684320*T - 311467391228
$97$
\( T^{4} + 2016 T^{3} + \cdots - 580580611196 \)
T^4 + 2016*T^3 - 752260*T^2 - 2679572160*T - 580580611196
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