[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
\( T_{3}^{7} + 3T_{3}^{6} - 8T_{3}^{5} - 20T_{3}^{4} + 22T_{3}^{3} + 24T_{3}^{2} - 31T_{3} + 8 \)
T3^7 + 3*T3^6 - 8*T3^5 - 20*T3^4 + 22*T3^3 + 24*T3^2 - 31*T3 + 8
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4030))\).
$p$
$F_p(T)$
$2$
\( (T - 1)^{7} \)
(T - 1)^7
$3$
\( T^{7} + 3 T^{6} - 8 T^{5} - 20 T^{4} + \cdots + 8 \)
T^7 + 3*T^6 - 8*T^5 - 20*T^4 + 22*T^3 + 24*T^2 - 31*T + 8
$5$
\( (T + 1)^{7} \)
(T + 1)^7
$7$
\( T^{7} - 4 T^{6} - 20 T^{5} + 64 T^{4} + \cdots - 8 \)
T^7 - 4*T^6 - 20*T^5 + 64*T^4 + 142*T^3 - 229*T^2 - 361*T - 8
$11$
\( T^{7} + 10 T^{6} + 9 T^{5} - 158 T^{4} + \cdots + 730 \)
T^7 + 10*T^6 + 9*T^5 - 158*T^4 - 340*T^3 + 542*T^2 + 1581*T + 730
$13$
\( (T + 1)^{7} \)
(T + 1)^7
$17$
\( T^{7} + 6 T^{6} - 53 T^{5} + \cdots - 1780 \)
T^7 + 6*T^6 - 53*T^5 - 248*T^4 + 1061*T^3 + 2669*T^2 - 8263*T - 1780
$19$
\( T^{7} + 5 T^{6} - 59 T^{5} + \cdots + 1168 \)
T^7 + 5*T^6 - 59*T^5 - 382*T^4 + 41*T^3 + 3448*T^2 + 5133*T + 1168
$23$
\( T^{7} + 11 T^{6} - 32 T^{5} + \cdots - 12898 \)
T^7 + 11*T^6 - 32*T^5 - 554*T^4 - 145*T^3 + 6445*T^2 + 5155*T - 12898
$29$
\( T^{7} + 18 T^{6} + 15 T^{5} + \cdots + 17044 \)
T^7 + 18*T^6 + 15*T^5 - 1284*T^4 - 6691*T^3 + 75*T^2 + 39777*T + 17044
$31$
\( (T - 1)^{7} \)
(T - 1)^7
$37$
\( T^{7} + 8 T^{6} - 39 T^{5} - 280 T^{4} + \cdots - 718 \)
T^7 + 8*T^6 - 39*T^5 - 280*T^4 + 598*T^3 + 2152*T^2 - 3671*T - 718
$41$
\( T^{7} + 12 T^{6} - 155 T^{5} + \cdots - 727682 \)
T^7 + 12*T^6 - 155*T^5 - 2119*T^4 + 2786*T^3 + 74605*T^2 + 11969*T - 727682
$43$
\( T^{7} + 5 T^{6} - 89 T^{5} - 116 T^{4} + \cdots + 400 \)
T^7 + 5*T^6 - 89*T^5 - 116*T^4 + 1735*T^3 - 3256*T^2 + 1499*T + 400
$47$
\( T^{7} + 10 T^{6} - 164 T^{5} + \cdots - 296060 \)
T^7 + 10*T^6 - 164*T^5 - 1200*T^4 + 8374*T^3 + 36185*T^2 - 99969*T - 296060
$53$
\( T^{7} + 18 T^{6} - 79 T^{5} + \cdots - 1550 \)
T^7 + 18*T^6 - 79*T^5 - 2451*T^4 - 4260*T^3 + 43655*T^2 + 23279*T - 1550
$59$
\( T^{7} + 11 T^{6} - 96 T^{5} + \cdots - 11432 \)
T^7 + 11*T^6 - 96*T^5 - 1094*T^4 + 85*T^3 + 9891*T^2 + 1333*T - 11432
$61$
\( T^{7} + 25 T^{6} - 9 T^{5} + \cdots + 169768 \)
T^7 + 25*T^6 - 9*T^5 - 3856*T^4 - 17864*T^3 + 108879*T^2 + 659623*T + 169768
$67$
\( T^{7} + 22 T^{6} - 66 T^{5} + \cdots + 3085532 \)
T^7 + 22*T^6 - 66*T^5 - 4262*T^4 - 19052*T^3 + 167491*T^2 + 1495321*T + 3085532
$71$
\( T^{7} + 22 T^{6} + 35 T^{5} + \cdots - 147320 \)
T^7 + 22*T^6 + 35*T^5 - 1540*T^4 - 3145*T^3 + 38950*T^2 - 731*T - 147320
$73$
\( T^{7} - 19 T^{6} - 219 T^{5} + \cdots - 1544548 \)
T^7 - 19*T^6 - 219*T^5 + 5588*T^4 - 1802*T^3 - 395697*T^2 + 1766451*T - 1544548
$79$
\( T^{7} + 20 T^{6} - 169 T^{5} + \cdots + 150364 \)
T^7 + 20*T^6 - 169*T^5 - 4574*T^4 - 540*T^3 + 257372*T^2 + 789089*T + 150364
$83$
\( T^{7} + 8 T^{6} - 388 T^{5} + \cdots - 1088852 \)
T^7 + 8*T^6 - 388*T^5 - 3320*T^4 + 36304*T^3 + 318367*T^2 - 171715*T - 1088852
$89$
\( T^{7} + 4 T^{6} - 401 T^{5} + \cdots + 907502 \)
T^7 + 4*T^6 - 401*T^5 - 888*T^4 + 49611*T^3 + 34663*T^2 - 1861903*T + 907502
$97$
\( T^{7} - 13 T^{6} - 232 T^{5} + \cdots + 967030 \)
T^7 - 13*T^6 - 232*T^5 + 3187*T^4 + 5149*T^3 - 127238*T^2 + 50459*T + 967030
show more
show less