[N,k,chi] = [138,6,Mod(1,138)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(138, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("138.1");
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
\(2\)
\(-1\)
\(3\)
\(-1\)
\(23\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{4} - 54T_{5}^{3} - 9218T_{5}^{2} + 613004T_{5} - 9068808 \)
T5^4 - 54*T5^3 - 9218*T5^2 + 613004*T5 - 9068808
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(138))\).
$p$
$F_p(T)$
$2$
\( (T - 4)^{4} \)
(T - 4)^4
$3$
\( (T - 9)^{4} \)
(T - 9)^4
$5$
\( T^{4} - 54 T^{3} - 9218 T^{2} + \cdots - 9068808 \)
T^4 - 54*T^3 - 9218*T^2 + 613004*T - 9068808
$7$
\( T^{4} - 348 T^{3} + \cdots - 247202152 \)
T^4 - 348*T^3 + 21258*T^2 + 2808840*T - 247202152
$11$
\( T^{4} + 6 T^{3} + \cdots + 6955214976 \)
T^4 + 6*T^3 - 346292*T^2 + 46102464*T + 6955214976
$13$
\( T^{4} - 1248 T^{3} + \cdots - 368203080832 \)
T^4 - 1248*T^3 - 726612*T^2 + 1285527360*T - 368203080832
$17$
\( T^{4} + 56 T^{3} + \cdots + 791612460000 \)
T^4 + 56*T^3 - 4061750*T^2 + 1400442600*T + 791612460000
$19$
\( T^{4} - 1530 T^{3} + \cdots + 12533606427240 \)
T^4 - 1530*T^3 - 7871358*T^2 + 7936539172*T + 12533606427240
$23$
\( (T - 529)^{4} \)
(T - 529)^4
$29$
\( T^{4} - 2292 T^{3} + \cdots - 7814693873520 \)
T^4 - 2292*T^3 - 15879560*T^2 + 23175942096*T - 7814693873520
$31$
\( T^{4} + \cdots + 270426164868224 \)
T^4 - 1556*T^3 - 52901480*T^2 + 62292852384*T + 270426164868224
$37$
\( T^{4} + 9586 T^{3} + \cdots - 30\!\cdots\!00 \)
T^4 + 9586*T^3 - 110151272*T^2 - 1275039507560*T - 3022090813986000
$41$
\( T^{4} + 11768 T^{3} + \cdots - 17\!\cdots\!40 \)
T^4 + 11768*T^3 - 155571016*T^2 - 1579238683808*T - 1731267316886640
$43$
\( T^{4} - 13758 T^{3} + \cdots + 12\!\cdots\!72 \)
T^4 - 13758*T^3 - 85863302*T^2 + 432081433292*T + 1288645968795672
$47$
\( T^{4} - 10636 T^{3} + \cdots + 17\!\cdots\!60 \)
T^4 - 10636*T^3 - 237779764*T^2 + 1444551005824*T + 17140752009360960
$53$
\( T^{4} - 26686 T^{3} + \cdots - 75\!\cdots\!00 \)
T^4 - 26686*T^3 - 480147434*T^2 + 14207821140044*T - 75365170064868600
$59$
\( T^{4} + 9108 T^{3} + \cdots + 21\!\cdots\!68 \)
T^4 + 9108*T^3 - 3083058644*T^2 - 7086464608608*T + 2148317951977003968
$61$
\( T^{4} + 37878 T^{3} + \cdots - 55\!\cdots\!20 \)
T^4 + 37878*T^3 - 70004496*T^2 - 10723403377368*T - 55033310263871920
$67$
\( T^{4} + 23302 T^{3} + \cdots + 38\!\cdots\!80 \)
T^4 + 23302*T^3 - 4208142726*T^2 - 67116245277852*T + 3837367640430461880
$71$
\( T^{4} - 31728 T^{3} + \cdots + 34\!\cdots\!00 \)
T^4 - 31728*T^3 - 4596389648*T^2 + 50467661767680*T + 3437299069314508800
$73$
\( T^{4} + 28340 T^{3} + \cdots + 61\!\cdots\!00 \)
T^4 + 28340*T^3 - 4351165456*T^2 + 33118038107120*T + 619572488883962800
$79$
\( T^{4} + 26668 T^{3} + \cdots + 42\!\cdots\!60 \)
T^4 + 26668*T^3 - 2176336646*T^2 + 10253764525432*T + 42551404111273560
$83$
\( T^{4} + 119026 T^{3} + \cdots - 77\!\cdots\!00 \)
T^4 + 119026*T^3 + 807964284*T^2 - 286794493543616*T - 7774539684526257600
$89$
\( T^{4} + 148236 T^{3} + \cdots - 32\!\cdots\!00 \)
T^4 + 148236*T^3 - 3298020230*T^2 - 1058166221366400*T - 32410527297737940000
$97$
\( T^{4} + 16092 T^{3} + \cdots + 16\!\cdots\!20 \)
T^4 + 16092*T^3 - 8616632120*T^2 + 170177146093904*T + 1640063762391571920
show more
show less