[N,k,chi] = [495,6,Mod(1,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("495.1");
S:= CuspForms(chi, 6);
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
\(3\)
\(-1\)
\(5\)
\(1\)
\(11\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} - 7T_{2}^{2} - 36T_{2} + 140 \)
T2^3 - 7*T2^2 - 36*T2 + 140
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(495))\).
$p$
$F_p(T)$
$2$
\( T^{3} - 7 T^{2} - 36 T + 140 \)
T^3 - 7*T^2 - 36*T + 140
$3$
\( T^{3} \)
T^3
$5$
\( (T + 25)^{3} \)
(T + 25)^3
$7$
\( T^{3} + 172 T^{2} + 2896 T - 382464 \)
T^3 + 172*T^2 + 2896*T - 382464
$11$
\( (T - 121)^{3} \)
(T - 121)^3
$13$
\( T^{3} + 654 T^{2} + \cdots - 317918392 \)
T^3 + 654*T^2 - 558788*T - 317918392
$17$
\( T^{3} - 2366 T^{2} + \cdots + 137826264 \)
T^3 - 2366*T^2 + 495212*T + 137826264
$19$
\( T^{3} + 2872 T^{2} + \cdots + 11543616 \)
T^3 + 2872*T^2 + 1821408*T + 11543616
$23$
\( T^{3} + 2272 T^{2} + \cdots - 3706904576 \)
T^3 + 2272*T^2 - 1259072*T - 3706904576
$29$
\( T^{3} - 7738 T^{2} + \cdots - 5220625848 \)
T^3 - 7738*T^2 + 14353100*T - 5220625848
$31$
\( T^{3} - 568 T^{2} + \cdots - 289787904 \)
T^3 - 568*T^2 - 1931712*T - 289787904
$37$
\( T^{3} + 9126 T^{2} + \cdots - 129972509048 \)
T^3 + 9126*T^2 - 54723956*T - 129972509048
$41$
\( T^{3} - 8758 T^{2} + \cdots + 1122652557432 \)
T^3 - 8758*T^2 - 230315700*T + 1122652557432
$43$
\( T^{3} + 14672 T^{2} + \cdots - 518908872384 \)
T^3 + 14672*T^2 - 70310304*T - 518908872384
$47$
\( T^{3} - 19392 T^{2} + \cdots + 1508908531200 \)
T^3 - 19392*T^2 - 35113856*T + 1508908531200
$53$
\( T^{3} - 4598 T^{2} + \cdots - 728896505288 \)
T^3 - 4598*T^2 - 354257972*T - 728896505288
$59$
\( T^{3} - 9348 T^{2} + \cdots + 6267836310080 \)
T^3 - 9348*T^2 - 498483344*T + 6267836310080
$61$
\( T^{3} + 60078 T^{2} + \cdots - 13500896397400 \)
T^3 + 60078*T^2 + 490851628*T - 13500896397400
$67$
\( T^{3} + 38468 T^{2} + \cdots - 8479952260160 \)
T^3 + 38468*T^2 - 183974416*T - 8479952260160
$71$
\( T^{3} - 74032 T^{2} + \cdots + 17011990639616 \)
T^3 - 74032*T^2 + 685830592*T + 17011990639616
$73$
\( T^{3} + 44442 T^{2} + \cdots - 9750515676328 \)
T^3 + 44442*T^2 + 111876700*T - 9750515676328
$79$
\( T^{3} + 108116 T^{2} + \cdots + 9069370346752 \)
T^3 + 108116*T^2 + 1927505936*T + 9069370346752
$83$
\( T^{3} + \cdots + 739830059345664 \)
T^3 - 81892*T^2 - 9807165024*T + 739830059345664
$89$
\( T^{3} + \cdots + 158914472576552 \)
T^3 + 167342*T^2 + 9085751148*T + 158914472576552
$97$
\( T^{3} + \cdots + 352998320493112 \)
T^3 - 159702*T^2 + 2383543948*T + 352998320493112
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