[N,k,chi] = [1875,2,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1875.1");
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
\(3\)
\(-1\)
\(5\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{6} - 11T_{2}^{4} - T_{2}^{3} + 29T_{2}^{2} + 3T_{2} - 1 \)
T2^6 - 11*T2^4 - T2^3 + 29*T2^2 + 3*T2 - 1
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1875))\).
$p$
$F_p(T)$
$2$
\( T^{6} - 11 T^{4} - T^{3} + 29 T^{2} + \cdots - 1 \)
T^6 - 11*T^4 - T^3 + 29*T^2 + 3*T - 1
$3$
\( (T - 1)^{6} \)
(T - 1)^6
$5$
\( T^{6} \)
T^6
$7$
\( T^{6} - 6 T^{5} + 4 T^{4} + 25 T^{3} + \cdots + 20 \)
T^6 - 6*T^5 + 4*T^4 + 25*T^3 - 25*T^2 - 20*T + 20
$11$
\( T^{6} - 3 T^{5} - 24 T^{4} + 66 T^{3} + \cdots + 244 \)
T^6 - 3*T^5 - 24*T^4 + 66*T^3 + 111*T^2 - 390*T + 244
$13$
\( T^{6} - 6 T^{5} - 26 T^{4} + 173 T^{3} + \cdots + 101 \)
T^6 - 6*T^5 - 26*T^4 + 173*T^3 + 101*T^2 - 985*T + 101
$17$
\( T^{6} - 13 T^{5} + 15 T^{4} + \cdots + 4639 \)
T^6 - 13*T^5 + 15*T^4 + 425*T^3 - 1810*T^2 + 622*T + 4639
$19$
\( T^{6} - 11 T^{5} + 11 T^{4} + \cdots - 380 \)
T^6 - 11*T^5 + 11*T^4 + 169*T^3 - 199*T^2 - 750*T - 380
$23$
\( T^{6} - 13 T^{5} + 6 T^{4} + \cdots - 2020 \)
T^6 - 13*T^5 + 6*T^4 + 310*T^3 - 115*T^2 - 2120*T - 2020
$29$
\( T^{6} + 3 T^{5} - 41 T^{4} + \cdots + 2105 \)
T^6 + 3*T^5 - 41*T^4 - 173*T^3 + 226*T^2 + 1830*T + 2105
$31$
\( T^{6} + 11 T^{5} - 46 T^{4} + \cdots - 2900 \)
T^6 + 11*T^5 - 46*T^4 - 680*T^3 - 485*T^2 + 4050*T - 2900
$37$
\( T^{6} - 21 T^{5} + 139 T^{4} + \cdots - 6025 \)
T^6 - 21*T^5 + 139*T^4 - 115*T^3 - 2140*T^2 + 7400*T - 6025
$41$
\( T^{6} + T^{5} - 181 T^{4} + \cdots - 82655 \)
T^6 + T^5 - 181*T^4 + 110*T^3 + 8995*T^2 - 13455*T - 82655
$43$
\( T^{6} - 2 T^{5} - 91 T^{4} + \cdots - 6284 \)
T^6 - 2*T^5 - 91*T^4 + 174*T^3 + 1369*T^2 - 1422*T - 6284
$47$
\( T^{6} - 14 T^{5} - 4 T^{4} + \cdots + 2284 \)
T^6 - 14*T^5 - 4*T^4 + 687*T^3 - 2311*T^2 + 906*T + 2284
$53$
\( T^{6} - 23 T^{5} + 61 T^{4} + \cdots - 34495 \)
T^6 - 23*T^5 + 61*T^4 + 1785*T^3 - 14430*T^2 + 38570*T - 34495
$59$
\( T^{6} - 9 T^{5} - 89 T^{4} + \cdots + 3920 \)
T^6 - 9*T^5 - 89*T^4 + 391*T^3 + 1231*T^2 - 5040*T + 3920
$61$
\( T^{6} - 11 T^{5} - 139 T^{4} + \cdots + 168269 \)
T^6 - 11*T^5 - 139*T^4 + 1848*T^3 + 1389*T^2 - 67021*T + 168269
$67$
\( T^{6} - 8 T^{5} - 155 T^{4} + \cdots + 14684 \)
T^6 - 8*T^5 - 155*T^4 + 1390*T^3 + 755*T^2 - 13038*T + 14684
$71$
\( T^{6} + 8 T^{5} - 150 T^{4} + \cdots - 196 \)
T^6 + 8*T^5 - 150*T^4 - 1745*T^3 - 5155*T^2 - 3122*T - 196
$73$
\( T^{6} - 13 T^{5} - 74 T^{4} + \cdots + 22205 \)
T^6 - 13*T^5 - 74*T^4 + 1175*T^3 - 270*T^2 - 14825*T + 22205
$79$
\( T^{6} + 5 T^{5} - 160 T^{4} + \cdots - 8000 \)
T^6 + 5*T^5 - 160*T^4 - 530*T^3 + 1955*T^2 + 3800*T - 8000
$83$
\( T^{6} + 20 T^{5} + 26 T^{4} + \cdots + 41036 \)
T^6 + 20*T^5 + 26*T^4 - 1252*T^3 - 5031*T^2 + 7744*T + 41036
$89$
\( T^{6} + 4 T^{5} - 464 T^{4} + \cdots - 377055 \)
T^6 + 4*T^5 - 464*T^4 - 131*T^3 + 55441*T^2 - 197505*T - 377055
$97$
\( T^{6} + 7 T^{5} - 215 T^{4} + \cdots + 2399 \)
T^6 + 7*T^5 - 215*T^4 - 1490*T^3 + 11495*T^2 + 78987*T + 2399
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