[N,k,chi] = [2169,2,Mod(1,2169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2169, 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("2169.1");
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
\(3\)
\(-1\)
\(241\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{5} - 2T_{2}^{4} - 4T_{2}^{3} + 7T_{2}^{2} + 4T_{2} - 5 \)
T2^5 - 2*T2^4 - 4*T2^3 + 7*T2^2 + 4*T2 - 5
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2169))\).
$p$
$F_p(T)$
$2$
\( T^{5} - 2 T^{4} - 4 T^{3} + 7 T^{2} + \cdots - 5 \)
T^5 - 2*T^4 - 4*T^3 + 7*T^2 + 4*T - 5
$3$
\( T^{5} \)
T^5
$5$
\( T^{5} - 8 T^{4} + 18 T^{3} + T^{2} + \cdots + 25 \)
T^5 - 8*T^4 + 18*T^3 + T^2 - 38*T + 25
$7$
\( T^{5} + 7 T^{4} + 4 T^{3} - 45 T^{2} + \cdots - 23 \)
T^5 + 7*T^4 + 4*T^3 - 45*T^2 - 65*T - 23
$11$
\( T^{5} + 2 T^{4} - 43 T^{3} + \cdots + 1241 \)
T^5 + 2*T^4 - 43*T^3 - 101*T^2 + 465*T + 1241
$13$
\( T^{5} + 20 T^{4} + 149 T^{3} + \cdots + 305 \)
T^5 + 20*T^4 + 149*T^3 + 504*T^2 + 732*T + 305
$17$
\( T^{5} - 4 T^{4} - 31 T^{3} + 64 T^{2} + \cdots + 157 \)
T^5 - 4*T^4 - 31*T^3 + 64*T^2 + 306*T + 157
$19$
\( T^{5} + 7 T^{4} - 51 T^{3} - 222 T^{2} + \cdots + 149 \)
T^5 + 7*T^4 - 51*T^3 - 222*T^2 + 867*T + 149
$23$
\( T^{5} + 6 T^{4} - 40 T^{3} - 139 T^{2} + \cdots + 629 \)
T^5 + 6*T^4 - 40*T^3 - 139*T^2 + 270*T + 629
$29$
\( T^{5} + 5 T^{4} - 70 T^{3} + \cdots + 2161 \)
T^5 + 5*T^4 - 70*T^3 - 294*T^2 + 917*T + 2161
$31$
\( T^{5} + 31 T^{4} + 348 T^{3} + \cdots - 3923 \)
T^5 + 31*T^4 + 348*T^3 + 1599*T^2 + 1805*T - 3923
$37$
\( T^{5} + 17 T^{4} + 83 T^{3} + \cdots - 485 \)
T^5 + 17*T^4 + 83*T^3 + 45*T^2 - 448*T - 485
$41$
\( T^{5} - 2 T^{4} - 98 T^{3} + \cdots + 3673 \)
T^5 - 2*T^4 - 98*T^3 - 7*T^2 + 2182*T + 3673
$43$
\( T^{5} + T^{4} - 174 T^{3} - 239 T^{2} + \cdots - 7603 \)
T^5 + T^4 - 174*T^3 - 239*T^2 + 5327*T - 7603
$47$
\( T^{5} - 21 T^{4} + 141 T^{3} + \cdots + 131 \)
T^5 - 21*T^4 + 141*T^3 - 267*T^2 - 256*T + 131
$53$
\( T^{5} + T^{4} - 247 T^{3} - 21 T^{2} + \cdots - 9719 \)
T^5 + T^4 - 247*T^3 - 21*T^2 + 13980*T - 9719
$59$
\( T^{5} + 3 T^{4} - 66 T^{3} + \cdots - 1285 \)
T^5 + 3*T^4 - 66*T^3 + 34*T^2 + 769*T - 1285
$61$
\( T^{5} + T^{4} - 157 T^{3} - 119 T^{2} + \cdots + 2069 \)
T^5 + T^4 - 157*T^3 - 119*T^2 + 3384*T + 2069
$67$
\( T^{5} + 9 T^{4} - 104 T^{3} + \cdots + 557 \)
T^5 + 9*T^4 - 104*T^3 - 1005*T^2 - 1667*T + 557
$71$
\( T^{5} - 4 T^{4} - 91 T^{3} + \cdots - 3307 \)
T^5 - 4*T^4 - 91*T^3 + 389*T^2 + 1057*T - 3307
$73$
\( T^{5} + 6 T^{4} - 247 T^{3} + \cdots - 41549 \)
T^5 + 6*T^4 - 247*T^3 - 248*T^2 + 15510*T - 41549
$79$
\( T^{5} + 17 T^{4} - 43 T^{3} + \cdots + 991 \)
T^5 + 17*T^4 - 43*T^3 - 954*T^2 - 703*T + 991
$83$
\( T^{5} - T^{4} - 201 T^{3} - 897 T^{2} + \cdots + 1579 \)
T^5 - T^4 - 201*T^3 - 897*T^2 + 4*T + 1579
$89$
\( T^{5} - 3 T^{4} - 161 T^{3} + \cdots - 21487 \)
T^5 - 3*T^4 - 161*T^3 + 486*T^2 + 5689*T - 21487
$97$
\( T^{5} + 30 T^{4} + 100 T^{3} + \cdots + 3463 \)
T^5 + 30*T^4 + 100*T^3 - 1903*T^2 + 3012*T + 3463
show more
show less