[N,k,chi] = [798,4,Mod(1,798)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(798, 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("798.1");
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
\(2\)
\(1\)
\(3\)
\(1\)
\(7\)
\(1\)
\(19\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{4} - 310T_{5}^{2} - 1444T_{5} - 1712 \)
T5^4 - 310*T5^2 - 1444*T5 - 1712
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(798))\).
$p$
$F_p(T)$
$2$
\( (T + 2)^{4} \)
(T + 2)^4
$3$
\( (T + 3)^{4} \)
(T + 3)^4
$5$
\( T^{4} - 310 T^{2} - 1444 T - 1712 \)
T^4 - 310*T^2 - 1444*T - 1712
$7$
\( (T + 7)^{4} \)
(T + 7)^4
$11$
\( T^{4} + 66 T^{3} - 2344 T^{2} + \cdots + 2890368 \)
T^4 + 66*T^3 - 2344*T^2 - 111968*T + 2890368
$13$
\( T^{4} - 10 T^{3} - 2328 T^{2} + \cdots - 142784 \)
T^4 - 10*T^3 - 2328*T^2 - 36720*T - 142784
$17$
\( T^{4} + 8 T^{3} - 12670 T^{2} + \cdots + 16113232 \)
T^4 + 8*T^3 - 12670*T^2 - 106740*T + 16113232
$19$
\( (T + 19)^{4} \)
(T + 19)^4
$23$
\( T^{4} + 250 T^{3} + \cdots - 47310976 \)
T^4 + 250*T^3 - 136*T^2 - 2431392*T - 47310976
$29$
\( T^{4} + 66 T^{3} - 36118 T^{2} + \cdots - 8975720 \)
T^4 + 66*T^3 - 36118*T^2 - 3278560*T - 8975720
$31$
\( T^{4} + 52 T^{3} - 25084 T^{2} + \cdots + 17593664 \)
T^4 + 52*T^3 - 25084*T^2 - 1597920*T + 17593664
$37$
\( T^{4} - 288 T^{3} + \cdots - 48733168 \)
T^4 - 288*T^3 - 41672*T^2 + 9877504*T - 48733168
$41$
\( T^{4} + 196 T^{3} + \cdots + 10624565808 \)
T^4 + 196*T^3 - 281104*T^2 - 52636688*T + 10624565808
$43$
\( T^{4} + 280 T^{3} + \cdots + 4071975168 \)
T^4 + 280*T^3 - 232940*T^2 - 62627728*T + 4071975168
$47$
\( T^{4} - 498 T^{3} + \cdots + 26000594272 \)
T^4 - 498*T^3 - 280162*T^2 + 91020304*T + 26000594272
$53$
\( T^{4} + 250 T^{3} + \cdots + 4988930584 \)
T^4 + 250*T^3 - 316326*T^2 + 13875808*T + 4988930584
$59$
\( T^{4} + 872 T^{3} + \cdots - 29703974400 \)
T^4 + 872*T^3 - 55536*T^2 - 170559360*T - 29703974400
$61$
\( T^{4} - 600 T^{3} + \cdots - 58773525616 \)
T^4 - 600*T^3 - 473096*T^2 + 371736352*T - 58773525616
$67$
\( T^{4} - 1174 T^{3} + \cdots - 332230224448 \)
T^4 - 1174*T^3 - 632104*T^2 + 1158131888*T - 332230224448
$71$
\( T^{4} + 1766 T^{3} + \cdots - 29250994688 \)
T^4 + 1766*T^3 + 900902*T^2 + 74288208*T - 29250994688
$73$
\( T^{4} - 556 T^{3} + \cdots - 19075973488 \)
T^4 - 556*T^3 - 418168*T^2 + 249100112*T - 19075973488
$79$
\( T^{4} - 26 T^{3} + \cdots + 177158677760 \)
T^4 - 26*T^3 - 1474936*T^2 + 401096320*T + 177158677760
$83$
\( T^{4} - 674 T^{3} + \cdots - 3506323104 \)
T^4 - 674*T^3 + 4686*T^2 + 45982544*T - 3506323104
$89$
\( T^{4} + 324 T^{3} + \cdots + 1900008394800 \)
T^4 + 324*T^3 - 2772688*T^2 - 413102480*T + 1900008394800
$97$
\( T^{4} - 2902 T^{3} + \cdots - 106797711936 \)
T^4 - 2902*T^3 + 2121612*T^2 - 204486056*T - 106797711936
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