[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, 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("825.1");
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
\(3\)
\(-1\)
\(5\)
\(1\)
\(11\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} + 7T_{2}^{2} - 60T_{2} - 308 \)
T2^3 + 7*T2^2 - 60*T2 - 308
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(825))\).
$p$
$F_p(T)$
$2$
\( T^{3} + 7 T^{2} - 60 T - 308 \)
T^3 + 7*T^2 - 60*T - 308
$3$
\( (T - 9)^{3} \)
(T - 9)^3
$5$
\( T^{3} \)
T^3
$7$
\( T^{3} + 92 T^{2} - 21932 T - 2026368 \)
T^3 + 92*T^2 - 21932*T - 2026368
$11$
\( (T - 121)^{3} \)
(T - 121)^3
$13$
\( T^{3} - 90 T^{2} + \cdots - 210673232 \)
T^3 - 90*T^2 - 975680*T - 210673232
$17$
\( T^{3} + 1934 T^{2} + \cdots - 123909408 \)
T^3 + 1934*T^2 + 810800*T - 123909408
$19$
\( T^{3} - 2084 T^{2} + \cdots + 14437440 \)
T^3 - 2084*T^2 + 1024056*T + 14437440
$23$
\( T^{3} + 1220 T^{2} + \cdots - 2404328128 \)
T^3 + 1220*T^2 - 5928368*T - 2404328128
$29$
\( T^{3} - 4402 T^{2} + \cdots + 80705567064 \)
T^3 - 4402*T^2 - 21861004*T + 80705567064
$31$
\( T^{3} + 10688 T^{2} + \cdots + 593236224 \)
T^3 + 10688*T^2 + 10258848*T + 593236224
$37$
\( T^{3} - 8190 T^{2} + \cdots + 165140256344 \)
T^3 - 8190*T^2 - 37082420*T + 165140256344
$41$
\( T^{3} - 5974 T^{2} + \cdots + 127610311752 \)
T^3 - 5974*T^2 - 48093036*T + 127610311752
$43$
\( T^{3} + 18868 T^{2} + \cdots - 5672527691040 \)
T^3 + 18868*T^2 - 310358172*T - 5672527691040
$47$
\( T^{3} + 55500 T^{2} + \cdots + 5576540180928 \)
T^3 + 55500*T^2 + 986474320*T + 5576540180928
$53$
\( T^{3} + 9206 T^{2} + \cdots + 850686588776 \)
T^3 + 9206*T^2 - 271155428*T + 850686588776
$59$
\( T^{3} + 59196 T^{2} + \cdots + 7185357358784 \)
T^3 + 59196*T^2 + 1143501904*T + 7185357358784
$61$
\( T^{3} - 79902 T^{2} + \cdots - 2993338614376 \)
T^3 - 79902*T^2 + 1647864172*T - 2993338614376
$67$
\( T^{3} + 4468 T^{2} + \cdots + 6432661987328 \)
T^3 + 4468*T^2 - 1336490752*T + 6432661987328
$71$
\( T^{3} + 75164 T^{2} + \cdots - 31171869026560 \)
T^3 + 75164*T^2 + 273188032*T - 31171869026560
$73$
\( T^{3} + \cdots + 152306824713328 \)
T^3 - 61290*T^2 - 2425659104*T + 152306824713328
$79$
\( T^{3} + \cdots - 283704612543488 \)
T^3 + 83564*T^2 - 3463328392*T - 283704612543488
$83$
\( T^{3} + \cdots - 200710881230832 \)
T^3 + 74764*T^2 - 2793564156*T - 200710881230832
$89$
\( T^{3} + \cdots + 340522035911288 \)
T^3 - 37342*T^2 - 7157973060*T + 340522035911288
$97$
\( T^{3} + 33486 T^{2} + \cdots + 93893760682568 \)
T^3 + 33486*T^2 - 5604419780*T + 93893760682568
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