[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
\( T_{2}^{3} - 2T_{2}^{2} - 60T_{2} + 88 \)
T2^3 - 2*T2^2 - 60*T2 + 88
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(825))\).
$p$
$F_p(T)$
$2$
\( T^{3} - 2 T^{2} - 60 T + 88 \)
T^3 - 2*T^2 - 60*T + 88
$3$
\( (T + 9)^{3} \)
(T + 9)^3
$5$
\( T^{3} \)
T^3
$7$
\( T^{3} - 232 T^{2} - 2132 T + 382608 \)
T^3 - 232*T^2 - 2132*T + 382608
$11$
\( (T - 121)^{3} \)
(T - 121)^3
$13$
\( T^{3} + 450 T^{2} + \cdots - 22659488 \)
T^3 + 450*T^2 - 45440*T - 22659488
$17$
\( T^{3} - 334 T^{2} + \cdots + 57782448 \)
T^3 - 334*T^2 - 261640*T + 57782448
$19$
\( T^{3} + 4036 T^{2} + \cdots - 1630951200 \)
T^3 + 4036*T^2 + 3118536*T - 1630951200
$23$
\( T^{3} - 7060 T^{2} + \cdots + 24275701568 \)
T^3 - 7060*T^2 + 5829232*T + 24275701568
$29$
\( T^{3} - 4042 T^{2} + \cdots + 65949214584 \)
T^3 - 4042*T^2 - 20041564*T + 65949214584
$31$
\( T^{3} + 608 T^{2} + \cdots - 211578448896 \)
T^3 + 608*T^2 - 90844992*T - 211578448896
$37$
\( T^{3} + 2250 T^{2} + \cdots + 431879868536 \)
T^3 + 2250*T^2 - 131985620*T + 431879868536
$41$
\( T^{3} - 10654 T^{2} + \cdots - 7803557208 \)
T^3 - 10654*T^2 + 20139204*T - 7803557208
$43$
\( T^{3} - 35528 T^{2} + \cdots - 1659712050000 \)
T^3 - 35528*T^2 + 420645228*T - 1659712050000
$47$
\( T^{3} - 2100 T^{2} + \cdots - 52162385088 \)
T^3 - 2100*T^2 - 94146320*T - 52162385088
$53$
\( T^{3} - 12826 T^{2} + \cdots - 2687939232856 \)
T^3 - 12826*T^2 - 834647588*T - 2687939232856
$59$
\( T^{3} + 81876 T^{2} + \cdots - 3633753791296 \)
T^3 + 81876*T^2 + 1502817904*T - 3633753791296
$61$
\( T^{3} + 62298 T^{2} + \cdots - 12904038746056 \)
T^3 + 62298*T^2 + 569911852*T - 12904038746056
$67$
\( T^{3} - 46148 T^{2} + \cdots + 40648408406912 \)
T^3 - 46148*T^2 - 761264032*T + 40648408406912
$71$
\( T^{3} + 64724 T^{2} + \cdots + 8578136735360 \)
T^3 + 64724*T^2 + 1324959712*T + 8578136735360
$73$
\( T^{3} + \cdots + 144432126809632 \)
T^3 + 810*T^2 - 5245925024*T + 144432126809632
$79$
\( T^{3} + \cdots + 351884592248992 \)
T^3 - 43876*T^2 - 9571579432*T + 351884592248992
$83$
\( T^{3} - 101024 T^{2} + \cdots - 5794291383408 \)
T^3 - 101024*T^2 + 1754366964*T - 5794291383408
$89$
\( T^{3} + \cdots - 246103360939432 \)
T^3 - 60022*T^2 - 10208967300*T - 246103360939432
$97$
\( T^{3} + \cdots - 179909862970168 \)
T^3 - 319746*T^2 + 25998829660*T - 179909862970168
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