[N,k,chi] = [802,2,Mod(1,802)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(802, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("802.1");
S:= CuspForms(chi, 2);
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
\(2\)
\(-1\)
\(401\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{5} + 6T_{3}^{4} + 9T_{3}^{3} - T_{3}^{2} - 5T_{3} + 1 \)
T3^5 + 6*T3^4 + 9*T3^3 - T3^2 - 5*T3 + 1
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(802))\).
$p$
$F_p(T)$
$2$
\( (T - 1)^{5} \)
(T - 1)^5
$3$
\( T^{5} + 6 T^{4} + 9 T^{3} - T^{2} - 5 T + 1 \)
T^5 + 6*T^4 + 9*T^3 - T^2 - 5*T + 1
$5$
\( T^{5} + 9 T^{4} + 26 T^{3} + 25 T^{2} + \cdots - 11 \)
T^5 + 9*T^4 + 26*T^3 + 25*T^2 - 3*T - 11
$7$
\( T^{5} + T^{4} - 17 T^{3} - 18 T^{2} + \cdots + 1 \)
T^5 + T^4 - 17*T^3 - 18*T^2 + 43*T + 1
$11$
\( T^{5} + 4 T^{4} - 25 T^{3} - 73 T^{2} + \cdots + 7 \)
T^5 + 4*T^4 - 25*T^3 - 73*T^2 + 99*T + 7
$13$
\( T^{5} + 9 T^{4} - 4 T^{3} - 173 T^{2} + \cdots + 823 \)
T^5 + 9*T^4 - 4*T^3 - 173*T^2 - 99*T + 823
$17$
\( T^{5} + 16 T^{4} + 96 T^{3} + 261 T^{2} + \cdots + 79 \)
T^5 + 16*T^4 + 96*T^3 + 261*T^2 + 296*T + 79
$19$
\( T^{5} + 8 T^{4} - 4 T^{3} - 185 T^{2} + \cdots - 433 \)
T^5 + 8*T^4 - 4*T^3 - 185*T^2 - 528*T - 433
$23$
\( T^{5} + 9 T^{4} - 7 T^{3} - 148 T^{2} + \cdots + 553 \)
T^5 + 9*T^4 - 7*T^3 - 148*T^2 + 13*T + 553
$29$
\( T^{5} + 8 T^{4} - 27 T^{3} + \cdots + 1831 \)
T^5 + 8*T^4 - 27*T^3 - 252*T^2 + 172*T + 1831
$31$
\( T^{5} + 6 T^{4} - 7 T^{3} - 82 T^{2} + \cdots + 79 \)
T^5 + 6*T^4 - 7*T^3 - 82*T^2 - 70*T + 79
$37$
\( T^{5} + 8 T^{4} - 52 T^{3} - 209 T^{2} + \cdots - 613 \)
T^5 + 8*T^4 - 52*T^3 - 209*T^2 + 978*T - 613
$41$
\( T^{5} + 15 T^{4} + 61 T^{3} + \cdots - 1451 \)
T^5 + 15*T^4 + 61*T^3 - 73*T^2 - 930*T - 1451
$43$
\( T^{5} - 3 T^{4} - 187 T^{3} + \cdots + 20239 \)
T^5 - 3*T^4 - 187*T^3 + 65*T^2 + 9388*T + 20239
$47$
\( T^{5} + 9 T^{4} - 64 T^{3} - 269 T^{2} + \cdots - 329 \)
T^5 + 9*T^4 - 64*T^3 - 269*T^2 + 1305*T - 329
$53$
\( T^{5} + 7 T^{4} - 72 T^{3} - 359 T^{2} + \cdots - 143 \)
T^5 + 7*T^4 - 72*T^3 - 359*T^2 + 549*T - 143
$59$
\( T^{5} + 6 T^{4} - 97 T^{3} - 808 T^{2} + \cdots - 539 \)
T^5 + 6*T^4 - 97*T^3 - 808*T^2 - 1424*T - 539
$61$
\( T^{5} + 7 T^{4} - 100 T^{3} + \cdots + 871 \)
T^5 + 7*T^4 - 100*T^3 - 547*T^2 + 747*T + 871
$67$
\( T^{5} + T^{4} - 277 T^{3} + \cdots + 16423 \)
T^5 + T^4 - 277*T^3 - 189*T^2 + 15330*T + 16423
$71$
\( T^{5} - 7 T^{4} - 54 T^{3} + \cdots - 1603 \)
T^5 - 7*T^4 - 54*T^3 + 293*T^2 + 403*T - 1603
$73$
\( T^{5} + 13 T^{4} - 41 T^{3} + \cdots - 1493 \)
T^5 + 13*T^4 - 41*T^3 - 715*T^2 - 2018*T - 1493
$79$
\( T^{5} - 37 T^{4} + 520 T^{3} + \cdots - 12649 \)
T^5 - 37*T^4 + 520*T^3 - 3447*T^2 + 10753*T - 12649
$83$
\( T^{5} + 10 T^{4} - 100 T^{3} + \cdots + 9007 \)
T^5 + 10*T^4 - 100*T^3 - 923*T^2 + 1612*T + 9007
$89$
\( T^{5} - 2 T^{4} - 63 T^{3} + 175 T^{2} + \cdots + 107 \)
T^5 - 2*T^4 - 63*T^3 + 175*T^2 + 305*T + 107
$97$
\( T^{5} + T^{4} - 355 T^{3} + \cdots + 79121 \)
T^5 + T^4 - 355*T^3 - 491*T^2 + 23022*T + 79121
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