[N,k,chi] = [4030,2,Mod(1,4030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4030, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4030.1");
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
\(2\)
\(-1\)
\(5\)
\(-1\)
\(13\)
\(-1\)
\(31\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{6} + 7T_{3}^{5} + 12T_{3}^{4} - 8T_{3}^{3} - 24T_{3}^{2} + 4T_{3} + 9 \)
T3^6 + 7*T3^5 + 12*T3^4 - 8*T3^3 - 24*T3^2 + 4*T3 + 9
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4030))\).
$p$
$F_p(T)$
$2$
\( (T - 1)^{6} \)
(T - 1)^6
$3$
\( T^{6} + 7 T^{5} + 12 T^{4} - 8 T^{3} + \cdots + 9 \)
T^6 + 7*T^5 + 12*T^4 - 8*T^3 - 24*T^2 + 4*T + 9
$5$
\( (T - 1)^{6} \)
(T - 1)^6
$7$
\( T^{6} + 8 T^{5} + 2 T^{4} - 98 T^{3} + \cdots + 99 \)
T^6 + 8*T^5 + 2*T^4 - 98*T^3 - 138*T^2 + 155*T + 99
$11$
\( T^{6} + 10 T^{5} + 3 T^{4} - 194 T^{3} + \cdots - 9 \)
T^6 + 10*T^5 + 3*T^4 - 194*T^3 - 404*T^2 + 142*T - 9
$13$
\( (T - 1)^{6} \)
(T - 1)^6
$17$
\( T^{6} + 14 T^{5} + 15 T^{4} + \cdots + 4001 \)
T^6 + 14*T^5 + 15*T^4 - 412*T^3 - 829*T^2 + 3337*T + 4001
$19$
\( T^{6} + 3 T^{5} - 19 T^{4} - 30 T^{3} + \cdots - 1 \)
T^6 + 3*T^5 - 19*T^4 - 30*T^3 + 107*T^2 - 16*T - 1
$23$
\( T^{6} + 13 T^{5} - 14 T^{4} + \cdots + 2231 \)
T^6 + 13*T^5 - 14*T^4 - 862*T^3 - 4061*T^2 - 5083*T + 2231
$29$
\( T^{6} + 8 T^{5} - 25 T^{4} - 228 T^{3} + \cdots + 659 \)
T^6 + 8*T^5 - 25*T^4 - 228*T^3 - 159*T^2 + 623*T + 659
$31$
\( (T - 1)^{6} \)
(T - 1)^6
$37$
\( T^{6} + 16 T^{5} - 63 T^{4} + \cdots - 5667 \)
T^6 + 16*T^5 - 63*T^4 - 2108*T^3 - 10272*T^2 - 15734*T - 5667
$41$
\( T^{6} + 10 T^{5} - 153 T^{4} + \cdots + 4637 \)
T^6 + 10*T^5 - 153*T^4 - 1195*T^3 + 6176*T^2 + 27271*T + 4637
$43$
\( T^{6} + 17 T^{5} - 9 T^{4} + \cdots + 19575 \)
T^6 + 17*T^5 - 9*T^4 - 1246*T^3 - 4521*T^2 + 4412*T + 19575
$47$
\( T^{6} + 14 T^{5} - 42 T^{4} + \cdots + 10211 \)
T^6 + 14*T^5 - 42*T^4 - 1124*T^3 - 2314*T^2 + 8543*T + 10211
$53$
\( T^{6} + 22 T^{5} + 39 T^{4} + \cdots + 49611 \)
T^6 + 22*T^5 + 39*T^4 - 1691*T^3 - 8310*T^2 + 9073*T + 49611
$59$
\( T^{6} + 23 T^{5} + 156 T^{4} + \cdots - 545 \)
T^6 + 23*T^5 + 156*T^4 + 206*T^3 - 747*T^2 - 1391*T - 545
$61$
\( T^{6} - 17 T^{5} + 13 T^{4} + \cdots - 19811 \)
T^6 - 17*T^5 + 13*T^4 + 1334*T^3 - 9752*T^2 + 25247*T - 19811
$67$
\( T^{6} + 16 T^{5} - 8 T^{4} + \cdots + 4219 \)
T^6 + 16*T^5 - 8*T^4 - 852*T^3 - 1048*T^2 + 9711*T + 4219
$71$
\( T^{6} - 2 T^{5} - 193 T^{4} + \cdots + 25113 \)
T^6 - 2*T^5 - 193*T^4 - 532*T^3 + 5415*T^2 + 24022*T + 25113
$73$
\( T^{6} + 7 T^{5} - 53 T^{4} + \cdots - 6875 \)
T^6 + 7*T^5 - 53*T^4 - 306*T^3 + 998*T^2 + 3087*T - 6875
$79$
\( T^{6} + 8 T^{5} - 137 T^{4} + \cdots - 8693 \)
T^6 + 8*T^5 - 137*T^4 - 792*T^3 + 4366*T^2 + 20664*T - 8693
$83$
\( T^{6} + 16 T^{5} - 370 T^{4} + \cdots + 1013007 \)
T^6 + 16*T^5 - 370*T^4 - 6356*T^3 + 25044*T^2 + 574583*T + 1013007
$89$
\( T^{6} + 32 T^{5} + 173 T^{4} + \cdots - 12799 \)
T^6 + 32*T^5 + 173*T^4 - 1998*T^3 - 7639*T^2 + 44487*T - 12799
$97$
\( T^{6} - 31 T^{5} + 180 T^{4} + \cdots + 13849 \)
T^6 - 31*T^5 + 180*T^4 + 1723*T^3 - 15201*T^2 + 20596*T + 13849
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