[N,k,chi] = [2500,2,Mod(1,2500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2500, 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("2500.1");
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
\(2\)
\(-1\)
\(5\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{6} - T_{3}^{5} - 14T_{3}^{4} + 3T_{3}^{3} + 49T_{3}^{2} + 34T_{3} + 4 \)
T3^6 - T3^5 - 14*T3^4 + 3*T3^3 + 49*T3^2 + 34*T3 + 4
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2500))\).
$p$
$F_p(T)$
$2$
\( T^{6} \)
T^6
$3$
\( T^{6} - T^{5} - 14 T^{4} + 3 T^{3} + \cdots + 4 \)
T^6 - T^5 - 14*T^4 + 3*T^3 + 49*T^2 + 34*T + 4
$5$
\( T^{6} \)
T^6
$7$
\( T^{6} + T^{5} - 29 T^{4} - 18 T^{3} + \cdots - 576 \)
T^6 + T^5 - 29*T^4 - 18*T^3 + 244*T^2 + 96*T - 576
$11$
\( T^{6} - 5 T^{5} - 35 T^{4} + 90 T^{3} + \cdots - 400 \)
T^6 - 5*T^5 - 35*T^4 + 90*T^3 + 480*T^2 + 200*T - 400
$13$
\( T^{6} + 11 T^{5} + 16 T^{4} + \cdots - 181 \)
T^6 + 11*T^5 + 16*T^4 - 193*T^3 - 816*T^2 - 989*T - 181
$17$
\( T^{6} + 12 T^{5} + 39 T^{4} - 4 T^{3} + \cdots + 36 \)
T^6 + 12*T^5 + 39*T^4 - 4*T^3 - 151*T^2 - 78*T + 36
$19$
\( T^{6} - 6 T^{5} - 35 T^{4} + \cdots + 3236 \)
T^6 - 6*T^5 - 35*T^4 + 250*T^3 + 85*T^2 - 2406*T + 3236
$23$
\( T^{6} + 3 T^{5} - 46 T^{4} + 59 T^{3} + \cdots - 64 \)
T^6 + 3*T^5 - 46*T^4 + 59*T^3 + 119*T^2 - 152*T - 64
$29$
\( T^{6} - 11 T^{5} - 30 T^{4} + \cdots + 1021 \)
T^6 - 11*T^5 - 30*T^4 + 505*T^3 - 110*T^2 - 4651*T + 1021
$31$
\( T^{6} - T^{5} - 80 T^{4} + 85 T^{3} + \cdots - 10124 \)
T^6 - T^5 - 80*T^4 + 85*T^3 + 1695*T^2 - 1076*T - 10124
$37$
\( T^{6} + 16 T^{5} + 36 T^{4} + \cdots + 1459 \)
T^6 + 16*T^5 + 36*T^4 - 368*T^3 - 1136*T^2 + 1316*T + 1459
$41$
\( T^{6} - 16 T^{5} + 35 T^{4} + \cdots + 6436 \)
T^6 - 16*T^5 + 35*T^4 + 400*T^3 - 1135*T^2 - 2446*T + 6436
$43$
\( T^{6} - 25 T^{5} + 185 T^{4} + \cdots + 6400 \)
T^6 - 25*T^5 + 185*T^4 - 140*T^3 - 2720*T^2 + 4800*T + 6400
$47$
\( T^{6} - 8 T^{5} - 31 T^{4} + 316 T^{3} + \cdots + 16 \)
T^6 - 8*T^5 - 31*T^4 + 316*T^3 + 29*T^2 - 2268*T + 16
$53$
\( T^{6} + 22 T^{5} + 114 T^{4} + \cdots + 1321 \)
T^6 + 22*T^5 + 114*T^4 - 174*T^3 - 1086*T^2 + 182*T + 1321
$59$
\( T^{6} - 12 T^{5} - 85 T^{4} + \cdots + 11404 \)
T^6 - 12*T^5 - 85*T^4 + 820*T^3 - 55*T^2 - 7982*T + 11404
$61$
\( T^{6} - 12 T^{5} - 140 T^{4} + \cdots + 40759 \)
T^6 - 12*T^5 - 140*T^4 + 1540*T^3 - 980*T^2 - 19812*T + 40759
$67$
\( T^{6} + 21 T^{5} - 29 T^{4} + \cdots + 241424 \)
T^6 + 21*T^5 - 29*T^4 - 2478*T^3 - 6936*T^2 + 64376*T + 241424
$71$
\( T^{6} - 8 T^{5} - 135 T^{4} + \cdots + 74484 \)
T^6 - 8*T^5 - 135*T^4 + 1170*T^3 + 3335*T^2 - 42738*T + 74484
$73$
\( T^{6} + 16 T^{5} - 44 T^{4} + \cdots - 65851 \)
T^6 + 16*T^5 - 44*T^4 - 1238*T^3 + 1464*T^2 + 27816*T - 65851
$79$
\( T^{6} + 2 T^{5} - 245 T^{4} + \cdots - 237196 \)
T^6 + 2*T^5 - 245*T^4 - 390*T^3 + 16365*T^2 + 18532*T - 237196
$83$
\( T^{6} + 3 T^{5} - 246 T^{4} + \cdots - 6004 \)
T^6 + 3*T^5 - 246*T^4 - 1311*T^3 + 4339*T^2 + 5718*T - 6004
$89$
\( T^{6} - 34 T^{5} + 355 T^{4} + \cdots - 7984 \)
T^6 - 34*T^5 + 355*T^4 - 910*T^3 - 3535*T^2 + 13656*T - 7984
$97$
\( T^{6} - 9 T^{5} - 214 T^{4} + \cdots + 349009 \)
T^6 - 9*T^5 - 214*T^4 + 2267*T^3 + 7894*T^2 - 136909*T + 349009
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