[N,k,chi] = [1480,2,Mod(1,1480)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1480, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1480.1");
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
\(2\)
\(1\)
\(5\)
\(-1\)
\(37\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{6} - T_{3}^{5} - 16T_{3}^{4} + 12T_{3}^{3} + 60T_{3}^{2} - 18T_{3} - 44 \)
T3^6 - T3^5 - 16*T3^4 + 12*T3^3 + 60*T3^2 - 18*T3 - 44
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1480))\).
$p$
$F_p(T)$
$2$
\( T^{6} \)
T^6
$3$
\( T^{6} - T^{5} - 16 T^{4} + 12 T^{3} + \cdots - 44 \)
T^6 - T^5 - 16*T^4 + 12*T^3 + 60*T^2 - 18*T - 44
$5$
\( (T - 1)^{6} \)
(T - 1)^6
$7$
\( T^{6} - 8 T^{5} + 7 T^{4} + 76 T^{3} + \cdots + 302 \)
T^6 - 8*T^5 + 7*T^4 + 76*T^3 - 144*T^2 - 138*T + 302
$11$
\( T^{6} - 33 T^{4} - 64 T^{3} + 80 T^{2} + \cdots - 96 \)
T^6 - 33*T^4 - 64*T^3 + 80*T^2 + 144*T - 96
$13$
\( T^{6} - 10 T^{5} + 4 T^{4} + 180 T^{3} + \cdots + 384 \)
T^6 - 10*T^5 + 4*T^4 + 180*T^3 - 260*T^2 - 648*T + 384
$17$
\( T^{6} - 3 T^{5} - 44 T^{4} + 160 T^{3} + \cdots - 464 \)
T^6 - 3*T^5 - 44*T^4 + 160*T^3 + 160*T^2 - 492*T - 464
$19$
\( T^{6} + 6 T^{5} - 18 T^{4} - 110 T^{3} + \cdots - 64 \)
T^6 + 6*T^5 - 18*T^4 - 110*T^3 + 110*T^2 + 412*T - 64
$23$
\( T^{6} - 4 T^{5} - 76 T^{4} + 304 T^{3} + \cdots - 576 \)
T^6 - 4*T^5 - 76*T^4 + 304*T^3 + 560*T^2 - 1920*T - 576
$29$
\( T^{6} - 3 T^{5} - 74 T^{4} - 64 T^{3} + \cdots + 32 \)
T^6 - 3*T^5 - 74*T^4 - 64*T^3 + 352*T^2 - 240*T + 32
$31$
\( T^{6} + 3 T^{5} - 92 T^{4} + \cdots + 5496 \)
T^6 + 3*T^5 - 92*T^4 - 268*T^3 + 1876*T^2 + 6762*T + 5496
$37$
\( (T + 1)^{6} \)
(T + 1)^6
$41$
\( T^{6} - 10 T^{5} - 123 T^{4} + \cdots + 81504 \)
T^6 - 10*T^5 - 123*T^4 + 1632*T^3 - 1216*T^2 - 33744*T + 81504
$43$
\( T^{6} + 11 T^{5} - 154 T^{4} + \cdots - 51488 \)
T^6 + 11*T^5 - 154*T^4 - 1800*T^3 + 1840*T^2 + 29136*T - 51488
$47$
\( T^{6} - 23 T^{5} + 128 T^{4} + \cdots - 37784 \)
T^6 - 23*T^5 + 128*T^4 + 732*T^3 - 10256*T^2 + 35826*T - 37784
$53$
\( T^{6} - 10 T^{5} - 39 T^{4} + \cdots + 1296 \)
T^6 - 10*T^5 - 39*T^4 + 392*T^3 + 232*T^2 - 3168*T + 1296
$59$
\( T^{6} - 6 T^{5} - 134 T^{4} + \cdots - 128 \)
T^6 - 6*T^5 - 134*T^4 + 1294*T^3 - 3566*T^2 + 2808*T - 128
$61$
\( T^{6} - T^{5} - 80 T^{4} + 368 T^{3} + \cdots + 576 \)
T^6 - T^5 - 80*T^4 + 368*T^3 - 224*T^2 - 816*T + 576
$67$
\( T^{6} + 4 T^{5} - 202 T^{4} + \cdots + 44544 \)
T^6 + 4*T^5 - 202*T^4 - 1474*T^3 + 2414*T^2 + 31680*T + 44544
$71$
\( T^{6} - 9 T^{5} - 74 T^{4} + \cdots + 4224 \)
T^6 - 9*T^5 - 74*T^4 + 504*T^3 + 1088*T^2 - 7488*T + 4224
$73$
\( T^{6} - 11 T^{5} - 252 T^{4} + \cdots - 300672 \)
T^6 - 11*T^5 - 252*T^4 + 1440*T^3 + 22832*T^2 + 1584*T - 300672
$79$
\( T^{6} + 14 T^{5} - 82 T^{4} + \cdots + 5632 \)
T^6 + 14*T^5 - 82*T^4 - 2378*T^3 - 13926*T^2 - 25088*T + 5632
$83$
\( T^{6} - 11 T^{5} - 146 T^{4} + \cdots - 9624 \)
T^6 - 11*T^5 - 146*T^4 + 684*T^3 + 8044*T^2 + 13086*T - 9624
$89$
\( T^{6} - 30 T^{5} + 48 T^{4} + \cdots + 1147008 \)
T^6 - 30*T^5 + 48*T^4 + 4880*T^3 - 26800*T^2 - 175584*T + 1147008
$97$
\( T^{6} - 29 T^{5} + 44 T^{4} + \cdots + 1463296 \)
T^6 - 29*T^5 + 44*T^4 + 4896*T^3 - 29136*T^2 - 200736*T + 1463296
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