[N,k,chi] = [546,8,Mod(1,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.1");
S:= CuspForms(chi, 8);
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
\(2\)
\(-1\)
\(3\)
\(-1\)
\(7\)
\(1\)
\(13\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{3} + 378T_{5}^{2} - 66705T_{5} + 2461550 \)
T5^3 + 378*T5^2 - 66705*T5 + 2461550
acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(546))\).
$p$
$F_p(T)$
$2$
\( (T - 8)^{3} \)
(T - 8)^3
$3$
\( (T - 27)^{3} \)
(T - 27)^3
$5$
\( T^{3} + 378 T^{2} - 66705 T + 2461550 \)
T^3 + 378*T^2 - 66705*T + 2461550
$7$
\( (T + 343)^{3} \)
(T + 343)^3
$11$
\( T^{3} + 6069 T^{2} + \cdots - 11019191384 \)
T^3 + 6069*T^2 - 723798*T - 11019191384
$13$
\( (T - 2197)^{3} \)
(T - 2197)^3
$17$
\( T^{3} + 12231 T^{2} + \cdots - 2540015942296 \)
T^3 + 12231*T^2 - 215823030*T - 2540015942296
$19$
\( T^{3} + 4836 T^{2} + \cdots + 26372444700364 \)
T^3 + 4836*T^2 - 1928692953*T + 26372444700364
$23$
\( T^{3} - 111606 T^{2} + \cdots - 29333382239720 \)
T^3 - 111606*T^2 + 3484216017*T - 29333382239720
$29$
\( T^{3} - 105414 T^{2} + \cdots + 26262769167062 \)
T^3 - 105414*T^2 + 1554144639*T + 26262769167062
$31$
\( T^{3} + 263061 T^{2} + \cdots - 48\!\cdots\!72 \)
T^3 + 263061*T^2 - 21110848968*T - 4854922162860672
$37$
\( T^{3} + 585969 T^{2} + \cdots - 14\!\cdots\!12 \)
T^3 + 585969*T^2 + 37852717278*T - 14934462179679712
$41$
\( T^{3} + 649608 T^{2} + \cdots - 20\!\cdots\!96 \)
T^3 + 649608*T^2 + 74557837116*T - 2018235088188896
$43$
\( T^{3} + 76182 T^{2} + \cdots + 13\!\cdots\!52 \)
T^3 + 76182*T^2 - 29154223647*T + 1324624289254652
$47$
\( T^{3} + 1269219 T^{2} + \cdots - 59\!\cdots\!00 \)
T^3 + 1269219*T^2 + 289180543920*T - 59068196171942400
$53$
\( T^{3} - 326511 T^{2} + \cdots - 33\!\cdots\!00 \)
T^3 - 326511*T^2 - 2428993691760*T - 330345946605923100
$59$
\( T^{3} + 3434316 T^{2} + \cdots - 17\!\cdots\!20 \)
T^3 + 3434316*T^2 + 1967081380224*T - 1724136331477029120
$61$
\( T^{3} + 1450497 T^{2} + \cdots - 47\!\cdots\!60 \)
T^3 + 1450497*T^2 - 1144624414932*T - 473622024839505860
$67$
\( T^{3} + 1302372 T^{2} + \cdots - 53\!\cdots\!76 \)
T^3 + 1302372*T^2 - 6382235429988*T - 5371743788767397776
$71$
\( T^{3} + 5186076 T^{2} + \cdots - 59\!\cdots\!00 \)
T^3 + 5186076*T^2 - 10278242919360*T - 59588707830950060800
$73$
\( T^{3} + 3662940 T^{2} + \cdots - 33\!\cdots\!34 \)
T^3 + 3662940*T^2 - 15218246092755*T - 33260598587214439434
$79$
\( T^{3} + 2950251 T^{2} + \cdots - 40\!\cdots\!32 \)
T^3 + 2950251*T^2 - 9686215757622*T - 405115690620691232
$83$
\( T^{3} + 13650225 T^{2} + \cdots + 22\!\cdots\!64 \)
T^3 + 13650225*T^2 + 41478315722754*T + 22446568528090507864
$89$
\( T^{3} - 6379533 T^{2} + \cdots + 77\!\cdots\!80 \)
T^3 - 6379533*T^2 - 32785770974004*T + 77220703793201299380
$97$
\( T^{3} + 18032235 T^{2} + \cdots - 67\!\cdots\!20 \)
T^3 + 18032235*T^2 - 28706252463252*T - 677111200402319326220
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