[N,k,chi] = [209,2,Mod(1,209)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(209, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("209.1");
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
\(11\)
\(-1\)
\(19\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{5} - 2T_{2}^{4} - 6T_{2}^{3} + 10T_{2}^{2} + 5T_{2} - 4 \)
T2^5 - 2*T2^4 - 6*T2^3 + 10*T2^2 + 5*T2 - 4
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(209))\).
$p$
$F_p(T)$
$2$
\( T^{5} - 2 T^{4} - 6 T^{3} + 10 T^{2} + \cdots - 4 \)
T^5 - 2*T^4 - 6*T^3 + 10*T^2 + 5*T - 4
$3$
\( T^{5} - T^{4} - 9 T^{3} + 11 T^{2} + \cdots - 1 \)
T^5 - T^4 - 9*T^3 + 11*T^2 + 7*T - 1
$5$
\( T^{5} + 5 T^{4} - 3 T^{3} - 33 T^{2} + \cdots + 19 \)
T^5 + 5*T^4 - 3*T^3 - 33*T^2 - 9*T + 19
$7$
\( T^{5} - 6 T^{4} - T^{3} + 62 T^{2} + \cdots + 64 \)
T^5 - 6*T^4 - T^3 + 62*T^2 - 119*T + 64
$11$
\( (T - 1)^{5} \)
(T - 1)^5
$13$
\( T^{5} - 4 T^{4} - 9 T^{3} + 26 T^{2} + \cdots + 2 \)
T^5 - 4*T^4 - 9*T^3 + 26*T^2 + 37*T + 2
$17$
\( T^{5} + 4 T^{4} - 32 T^{3} - 64 T^{2} + \cdots - 64 \)
T^5 + 4*T^4 - 32*T^3 - 64*T^2 + 304*T - 64
$19$
\( (T + 1)^{5} \)
(T + 1)^5
$23$
\( T^{5} - 3 T^{4} - 76 T^{3} + 388 T^{2} + \cdots - 784 \)
T^5 - 3*T^4 - 76*T^3 + 388*T^2 - 224*T - 784
$29$
\( T^{5} - 10 T^{4} - 37 T^{3} + \cdots + 490 \)
T^5 - 10*T^4 - 37*T^3 + 656*T^2 - 1827*T + 490
$31$
\( T^{5} - 11 T^{4} - 3 T^{3} + 193 T^{2} + \cdots - 757 \)
T^5 - 11*T^4 - 3*T^3 + 193*T^2 - 31*T - 757
$37$
\( T^{5} - T^{4} - 80 T^{3} + 104 T^{2} + \cdots - 3088 \)
T^5 - T^4 - 80*T^3 + 104*T^2 + 1520*T - 3088
$41$
\( T^{5} - 2 T^{4} - 189 T^{3} + \cdots - 4112 \)
T^5 - 2*T^4 - 189*T^3 + 252*T^2 + 7253*T - 4112
$43$
\( T^{5} - 20 T^{4} + 23 T^{3} + \cdots + 11266 \)
T^5 - 20*T^4 + 23*T^3 + 1640*T^2 - 9843*T + 11266
$47$
\( T^{5} + 20 T^{4} + 28 T^{3} + \cdots + 13184 \)
T^5 + 20*T^4 + 28*T^3 - 1088*T^2 - 2192*T + 13184
$53$
\( T^{5} + 14 T^{4} - 88 T^{3} + \cdots + 30304 \)
T^5 + 14*T^4 - 88*T^3 - 1392*T^2 + 1808*T + 30304
$59$
\( T^{5} - 3 T^{4} - 164 T^{3} + \cdots - 2000 \)
T^5 - 3*T^4 - 164*T^3 + 908*T^2 - 496*T - 2000
$61$
\( T^{5} + 10 T^{4} - 24 T^{3} + \cdots - 736 \)
T^5 + 10*T^4 - 24*T^3 - 464*T^2 - 1264*T - 736
$67$
\( T^{5} - 9 T^{4} - 195 T^{3} + \cdots + 17689 \)
T^5 - 9*T^4 - 195*T^3 + 827*T^2 + 10633*T + 17689
$71$
\( T^{5} - 23 T^{4} - 17 T^{3} + \cdots + 19081 \)
T^5 - 23*T^4 - 17*T^3 + 2929*T^2 - 14485*T + 19081
$73$
\( T^{5} - 340 T^{3} - 1168 T^{2} + \cdots + 155392 \)
T^5 - 340*T^3 - 1168*T^2 + 27728*T + 155392
$79$
\( T^{5} - 44 T^{4} + 748 T^{3} + \cdots - 36800 \)
T^5 - 44*T^4 + 748*T^3 - 6128*T^2 + 24176*T - 36800
$83$
\( T^{5} + 14 T^{4} - 69 T^{3} + \cdots - 3908 \)
T^5 + 14*T^4 - 69*T^3 - 1242*T^2 - 4103*T - 3908
$89$
\( T^{5} + 27 T^{4} + 268 T^{3} + \cdots + 320 \)
T^5 + 27*T^4 + 268*T^3 + 1168*T^2 + 1952*T + 320
$97$
\( T^{5} - 15 T^{4} - 124 T^{3} + \cdots - 37456 \)
T^5 - 15*T^4 - 124*T^3 + 2116*T^2 + 304*T - 37456
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