[N,k,chi] = [260,6,Mod(1,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, 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("260.1");
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
\(2\)
\(-1\)
\(5\)
\(-1\)
\(13\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{4} + 20T_{3}^{3} - 244T_{3}^{2} - 3752T_{3} + 23460 \)
T3^4 + 20*T3^3 - 244*T3^2 - 3752*T3 + 23460
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(260))\).
$p$
$F_p(T)$
$2$
\( T^{4} \)
T^4
$3$
\( T^{4} + 20 T^{3} - 244 T^{2} + \cdots + 23460 \)
T^4 + 20*T^3 - 244*T^2 - 3752*T + 23460
$5$
\( (T - 25)^{4} \)
(T - 25)^4
$7$
\( T^{4} + 24 T^{3} - 19272 T^{2} + \cdots + 87674192 \)
T^4 + 24*T^3 - 19272*T^2 - 262176*T + 87674192
$11$
\( T^{4} + 12 T^{3} + \cdots + 11345306516 \)
T^4 + 12*T^3 - 223380*T^2 - 54792*T + 11345306516
$13$
\( (T + 169)^{4} \)
(T + 169)^4
$17$
\( T^{4} + 416 T^{3} + \cdots - 2150418352 \)
T^4 + 416*T^3 - 499880*T^2 + 92612928*T - 2150418352
$19$
\( T^{4} + 644 T^{3} + \cdots - 109653949260 \)
T^4 + 644*T^3 - 3786596*T^2 - 3897682264*T - 109653949260
$23$
\( T^{4} - 1748 T^{3} + \cdots + 2466019063044 \)
T^4 - 1748*T^3 - 10888740*T^2 - 6348350808*T + 2466019063044
$29$
\( T^{4} + \cdots + 457208195704832 \)
T^4 + 4080*T^3 - 40210272*T^2 - 92723136000*T + 457208195704832
$31$
\( T^{4} + 1500 T^{3} + \cdots - 62395614060 \)
T^4 + 1500*T^3 - 10709364*T^2 - 6544924648*T - 62395614060
$37$
\( T^{4} + \cdots - 209287701681600 \)
T^4 + 3848*T^3 - 204449744*T^2 - 481278191680*T - 209287701681600
$41$
\( T^{4} + 17968 T^{3} + \cdots - 12\!\cdots\!12 \)
T^4 + 17968*T^3 - 38212040*T^2 - 1374019588864*T - 1205473550526512
$43$
\( T^{4} - 3020 T^{3} + \cdots - 22\!\cdots\!76 \)
T^4 - 3020*T^3 - 419666564*T^2 - 1963089811816*T - 2278308840593276
$47$
\( T^{4} + 12328 T^{3} + \cdots + 22\!\cdots\!80 \)
T^4 + 12328*T^3 - 952713032*T^2 - 6091486154976*T + 229834458096544080
$53$
\( T^{4} + 52672 T^{3} + \cdots + 10\!\cdots\!52 \)
T^4 + 52672*T^3 + 886358232*T^2 + 4774972418368*T + 1037920688515152
$59$
\( T^{4} + 58988 T^{3} + \cdots - 59\!\cdots\!20 \)
T^4 + 58988*T^3 - 379388004*T^2 - 57048152377096*T - 593825983616092620
$61$
\( T^{4} + 56736 T^{3} + \cdots + 48\!\cdots\!36 \)
T^4 + 56736*T^3 - 1522508896*T^2 - 82217240087040*T + 486604691610126336
$67$
\( T^{4} + 56480 T^{3} + \cdots - 53\!\cdots\!40 \)
T^4 + 56480*T^3 - 410003240*T^2 - 52990949799424*T - 530403216722006640
$71$
\( T^{4} + 68260 T^{3} + \cdots + 31\!\cdots\!40 \)
T^4 + 68260*T^3 - 3086930516*T^2 - 158520665341016*T + 3117049566637174740
$73$
\( T^{4} + 113000 T^{3} + \cdots - 62\!\cdots\!84 \)
T^4 + 113000*T^3 + 143330736*T^2 - 274155196882752*T - 6265234387065921984
$79$
\( T^{4} + 43640 T^{3} + \cdots + 57\!\cdots\!60 \)
T^4 + 43640*T^3 - 4367017424*T^2 + 20010318073408*T + 571371477530282560
$83$
\( T^{4} + 52248 T^{3} + \cdots - 85\!\cdots\!80 \)
T^4 + 52248*T^3 - 8813571272*T^2 - 650400298696992*T - 8561993136030575280
$89$
\( T^{4} + 114376 T^{3} + \cdots - 26\!\cdots\!04 \)
T^4 + 114376*T^3 + 1372624408*T^2 - 159026561124576*T - 2648623219253765104
$97$
\( T^{4} + 21432 T^{3} + \cdots + 73\!\cdots\!04 \)
T^4 + 21432*T^3 - 20643287304*T^2 + 133425056848224*T + 73674605570445916304
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