[N,k,chi] = [464,4,Mod(1,464)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(464, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("464.1");
S:= CuspForms(chi, 4);
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
\(2\)
\(-1\)
\(29\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{5} + 8T_{3}^{4} - 52T_{3}^{3} - 322T_{3}^{2} + 187T_{3} + 1042 \)
T3^5 + 8*T3^4 - 52*T3^3 - 322*T3^2 + 187*T3 + 1042
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(464))\).
$p$
$F_p(T)$
$2$
\( T^{5} \)
T^5
$3$
\( T^{5} + 8 T^{4} - 52 T^{3} + \cdots + 1042 \)
T^5 + 8*T^4 - 52*T^3 - 322*T^2 + 187*T + 1042
$5$
\( T^{5} - 10 T^{4} - 366 T^{3} + \cdots - 55534 \)
T^5 - 10*T^4 - 366*T^3 + 2904*T^2 + 21453*T - 55534
$7$
\( T^{5} + 40 T^{4} + 84 T^{3} + \cdots - 243968 \)
T^5 + 40*T^4 + 84*T^3 - 10768*T^2 - 100288*T - 243968
$11$
\( T^{5} + 12 T^{4} - 4892 T^{3} + \cdots - 30997958 \)
T^5 + 12*T^4 - 4892*T^3 - 50174*T^2 + 4398787*T - 30997958
$13$
\( T^{5} - 14 T^{4} - 7558 T^{3} + \cdots - 13078418 \)
T^5 - 14*T^4 - 7558*T^3 + 133312*T^2 + 1294565*T - 13078418
$17$
\( T^{5} - 66 T^{4} - 2444 T^{3} + \cdots + 19935872 \)
T^5 - 66*T^4 - 2444*T^3 + 205448*T^2 - 3694112*T + 19935872
$19$
\( T^{5} + 214 T^{4} + \cdots - 19441152 \)
T^5 + 214*T^4 + 15136*T^3 + 342272*T^2 - 1091328*T - 19441152
$23$
\( T^{5} + 164 T^{4} + \cdots + 7938109184 \)
T^5 + 164*T^4 - 18812*T^3 - 3316000*T^2 + 24181632*T + 7938109184
$29$
\( (T + 29)^{5} \)
(T + 29)^5
$31$
\( T^{5} + 420 T^{4} + 45552 T^{3} + \cdots + 2094346 \)
T^5 + 420*T^4 + 45552*T^3 + 1363354*T^2 - 5574361*T + 2094346
$37$
\( T^{5} - 378 T^{4} + \cdots + 23564115968 \)
T^5 - 378*T^4 - 69792*T^3 + 30918912*T^2 - 2452994048*T + 23564115968
$41$
\( T^{5} + 1158 T^{4} + \cdots + 59613728000 \)
T^5 + 1158*T^4 + 462908*T^3 + 74423880*T^2 + 4409752000*T + 59613728000
$43$
\( T^{5} - 204 T^{4} + \cdots - 198643410886 \)
T^5 - 204*T^4 - 94388*T^3 + 11715386*T^2 + 1855476667*T - 198643410886
$47$
\( T^{5} + 248 T^{4} + \cdots + 203435244846 \)
T^5 + 248*T^4 - 332696*T^3 - 76509294*T^2 + 8179300863*T + 203435244846
$53$
\( T^{5} + 554 T^{4} + \cdots - 786854101018 \)
T^5 + 554*T^4 - 38334*T^3 - 72740336*T^2 - 14144920995*T - 786854101018
$59$
\( T^{5} + 440 T^{4} + \cdots - 109032704000 \)
T^5 + 440*T^4 - 95868*T^3 - 42988400*T^2 - 4107227200*T - 109032704000
$61$
\( T^{5} - 618 T^{4} + \cdots + 2140697762176 \)
T^5 - 618*T^4 - 204156*T^3 + 206442728*T^2 - 41066569056*T + 2140697762176
$67$
\( T^{5} + 1164 T^{4} + \cdots + 39308070146048 \)
T^5 + 1164*T^4 - 251984*T^3 - 457331392*T^2 + 25268520960*T + 39308070146048
$71$
\( T^{5} - 692 T^{4} + \cdots - 98341318953856 \)
T^5 - 692*T^4 - 876848*T^3 + 572202480*T^2 + 153248941872*T - 98341318953856
$73$
\( T^{5} + 1950 T^{4} + \cdots + 7201878016 \)
T^5 + 1950*T^4 + 1168032*T^3 + 267870432*T^2 + 19306358272*T + 7201878016
$79$
\( T^{5} + \cdots + 240961986300538 \)
T^5 + 272*T^4 - 1497888*T^3 - 545111474*T^2 + 543174633815*T + 240961986300538
$83$
\( T^{5} + 512 T^{4} + \cdots - 6057622580224 \)
T^5 + 512*T^4 - 520156*T^3 - 118532752*T^2 + 85821473600*T - 6057622580224
$89$
\( T^{5} - 866 T^{4} + \cdots + 21549994365568 \)
T^5 - 866*T^4 - 852420*T^3 + 69193352*T^2 + 138056266176*T + 21549994365568
$97$
\( T^{5} - 1562 T^{4} + \cdots - 20480102175488 \)
T^5 - 1562*T^4 + 412988*T^3 + 290423688*T^2 - 81033100480*T - 20480102175488
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