[N,k,chi] = [804,2,Mod(1,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.1");
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
\(2\)
\(-1\)
\(3\)
\(-1\)
\(67\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{5} - 3T_{5}^{4} - 13T_{5}^{3} + 37T_{5}^{2} + 36T_{5} - 96 \)
T5^5 - 3*T5^4 - 13*T5^3 + 37*T5^2 + 36*T5 - 96
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(804))\).
$p$
$F_p(T)$
$2$
\( T^{5} \)
T^5
$3$
\( (T - 1)^{5} \)
(T - 1)^5
$5$
\( T^{5} - 3 T^{4} - 13 T^{3} + 37 T^{2} + \cdots - 96 \)
T^5 - 3*T^4 - 13*T^3 + 37*T^2 + 36*T - 96
$7$
\( T^{5} - 5 T^{4} - 17 T^{3} + 89 T^{2} + \cdots - 64 \)
T^5 - 5*T^4 - 17*T^3 + 89*T^2 - 64
$11$
\( T^{5} - 6 T^{4} - 16 T^{3} + 100 T^{2} + \cdots - 384 \)
T^5 - 6*T^4 - 16*T^3 + 100*T^2 + 72*T - 384
$13$
\( T^{5} - 4 T^{4} - 24 T^{3} + 60 T^{2} + \cdots + 32 \)
T^5 - 4*T^4 - 24*T^3 + 60*T^2 + 168*T + 32
$17$
\( T^{5} - T^{4} - 64 T^{3} + 44 T^{2} + \cdots - 1128 \)
T^5 - T^4 - 64*T^3 + 44*T^2 + 852*T - 1128
$19$
\( T^{5} - 13 T^{4} + 4 T^{3} + \cdots - 2896 \)
T^5 - 13*T^4 + 4*T^3 + 416*T^2 - 644*T - 2896
$23$
\( T^{5} - 60 T^{3} + 72 T^{2} + \cdots + 162 \)
T^5 - 60*T^3 + 72*T^2 + 297*T + 162
$29$
\( T^{5} - 3 T^{4} - 58 T^{3} + \cdots - 1152 \)
T^5 - 3*T^4 - 58*T^3 + 136*T^2 + 672*T - 1152
$31$
\( T^{5} - 3 T^{4} - 137 T^{3} + \cdots - 11104 \)
T^5 - 3*T^4 - 137*T^3 + 383*T^2 + 3836*T - 11104
$37$
\( T^{5} - 12 T^{4} + 8 T^{3} + 246 T^{2} + \cdots + 346 \)
T^5 - 12*T^4 + 8*T^3 + 246*T^2 - 581*T + 346
$41$
\( T^{5} - 11 T^{4} - 111 T^{3} + \cdots - 22368 \)
T^5 - 11*T^4 - 111*T^3 + 1463*T^2 - 252*T - 22368
$43$
\( T^{5} - 3 T^{4} - 107 T^{3} + \cdots - 1096 \)
T^5 - 3*T^4 - 107*T^3 + 383*T^2 + 1214*T - 1096
$47$
\( T^{5} + 13 T^{4} - 112 T^{3} + \cdots + 19128 \)
T^5 + 13*T^4 - 112*T^3 - 1844*T^2 - 2484*T + 19128
$53$
\( T^{5} + 9 T^{4} - 25 T^{3} - 233 T^{2} + \cdots - 72 \)
T^5 + 9*T^4 - 25*T^3 - 233*T^2 + 282*T - 72
$59$
\( T^{5} + 12 T^{4} - 42 T^{3} - 136 T^{2} + \cdots + 18 \)
T^5 + 12*T^4 - 42*T^3 - 136*T^2 - 69*T + 18
$61$
\( T^{5} - 4 T^{4} - 168 T^{3} + \cdots - 9136 \)
T^5 - 4*T^4 - 168*T^3 + 348*T^2 + 6288*T - 9136
$67$
\( (T - 1)^{5} \)
(T - 1)^5
$71$
\( T^{5} + 24 T^{4} + 200 T^{3} + \cdots + 192 \)
T^5 + 24*T^4 + 200*T^3 + 676*T^2 + 840*T + 192
$73$
\( T^{5} - 12 T^{4} - 8 T^{3} + 386 T^{2} + \cdots + 362 \)
T^5 - 12*T^4 - 8*T^3 + 386*T^2 - 985*T + 362
$79$
\( T^{5} + 4 T^{4} - 216 T^{3} + \cdots + 16384 \)
T^5 + 4*T^4 - 216*T^3 - 1360*T^2 + 1920*T + 16384
$83$
\( T^{5} + 27 T^{4} + 143 T^{3} + \cdots + 3336 \)
T^5 + 27*T^4 + 143*T^3 - 727*T^2 - 4566*T + 3336
$89$
\( T^{5} + 5 T^{4} - 130 T^{3} + \cdots - 2424 \)
T^5 + 5*T^4 - 130*T^3 - 1168*T^2 - 3012*T - 2424
$97$
\( T^{5} - 8 T^{4} - 348 T^{3} + \cdots - 26912 \)
T^5 - 8*T^4 - 348*T^3 + 2252*T^2 + 12648*T - 26912
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