[N,k,chi] = [501,2,Mod(1,501)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(501, 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("501.1");
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
\(3\)
\(-1\)
\(167\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{5} + 4T_{2}^{4} + T_{2}^{3} - 8T_{2}^{2} - 2T_{2} + 3 \)
T2^5 + 4*T2^4 + T2^3 - 8*T2^2 - 2*T2 + 3
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(501))\).
$p$
$F_p(T)$
$2$
\( T^{5} + 4 T^{4} + T^{3} - 8 T^{2} - 2 T + 3 \)
T^5 + 4*T^4 + T^3 - 8*T^2 - 2*T + 3
$3$
\( (T - 1)^{5} \)
(T - 1)^5
$5$
\( T^{5} + 9 T^{4} + 25 T^{3} + 12 T^{2} + \cdots - 37 \)
T^5 + 9*T^4 + 25*T^3 + 12*T^2 - 39*T - 37
$7$
\( T^{5} + 4 T^{4} - 15 T^{3} - 49 T^{2} + \cdots + 83 \)
T^5 + 4*T^4 - 15*T^3 - 49*T^2 + 55*T + 83
$11$
\( T^{5} + 15 T^{4} + 69 T^{3} + \cdots - 761 \)
T^5 + 15*T^4 + 69*T^3 + 36*T^2 - 447*T - 761
$13$
\( T^{5} - 41 T^{3} - 32 T^{2} + \cdots + 687 \)
T^5 - 41*T^3 - 32*T^2 + 412*T + 687
$17$
\( T^{5} + 11 T^{4} - 10 T^{3} + \cdots + 2203 \)
T^5 + 11*T^4 - 10*T^3 - 358*T^2 - 343*T + 2203
$19$
\( T^{5} + 16 T^{4} + 61 T^{3} + \cdots - 677 \)
T^5 + 16*T^4 + 61*T^3 - 102*T^2 - 756*T - 677
$23$
\( T^{5} + 9 T^{4} - T^{3} - 170 T^{2} + \cdots - 47 \)
T^5 + 9*T^4 - T^3 - 170*T^2 - 355*T - 47
$29$
\( T^{5} + T^{4} - 89 T^{3} - 146 T^{2} + \cdots - 157 \)
T^5 + T^4 - 89*T^3 - 146*T^2 + 639*T - 157
$31$
\( T^{5} + 18 T^{4} + 90 T^{3} + 79 T^{2} + \cdots - 23 \)
T^5 + 18*T^4 + 90*T^3 + 79*T^2 - 240*T - 23
$37$
\( T^{5} - 7 T^{4} - 77 T^{3} + \cdots + 1809 \)
T^5 - 7*T^4 - 77*T^3 + 230*T^2 + 1645*T + 1809
$41$
\( T^{5} + 10 T^{4} - 120 T^{3} + \cdots - 87 \)
T^5 + 10*T^4 - 120*T^3 - 1119*T^2 + 656*T - 87
$43$
\( T^{5} - 6 T^{4} - 126 T^{3} + \cdots - 127 \)
T^5 - 6*T^4 - 126*T^3 + 953*T^2 - 1118*T - 127
$47$
\( T^{5} + 7 T^{4} - 57 T^{3} + \cdots + 1209 \)
T^5 + 7*T^4 - 57*T^3 - 517*T^2 - 668*T + 1209
$53$
\( T^{5} + 9 T^{4} - 127 T^{3} + \cdots - 3061 \)
T^5 + 9*T^4 - 127*T^3 - 1725*T^2 - 5578*T - 3061
$59$
\( T^{5} + 37 T^{4} + 469 T^{3} + \cdots - 617 \)
T^5 + 37*T^4 + 469*T^3 + 2337*T^2 + 3846*T - 617
$61$
\( T^{5} + 2 T^{4} - 231 T^{3} + \cdots + 69523 \)
T^5 + 2*T^4 - 231*T^3 - 854*T^2 + 13540*T + 69523
$67$
\( T^{5} - 219 T^{3} + 558 T^{2} + \cdots + 751 \)
T^5 - 219*T^3 + 558*T^2 + 1608*T + 751
$71$
\( T^{5} - 13 T^{4} - 258 T^{3} + \cdots - 64423 \)
T^5 - 13*T^4 - 258*T^3 + 2677*T^2 + 14869*T - 64423
$73$
\( T^{5} + 6 T^{4} - 15 T^{3} - 40 T^{2} + \cdots - 3 \)
T^5 + 6*T^4 - 15*T^3 - 40*T^2 + 26*T - 3
$79$
\( T^{5} - 14 T^{4} + 44 T^{3} + \cdots + 923 \)
T^5 - 14*T^4 + 44*T^3 + 119*T^2 - 764*T + 923
$83$
\( T^{5} + 5 T^{4} - 169 T^{3} + \cdots - 10575 \)
T^5 + 5*T^4 - 169*T^3 - 1991*T^2 - 7840*T - 10575
$89$
\( T^{5} + 30 T^{4} + 217 T^{3} + \cdots - 55203 \)
T^5 + 30*T^4 + 217*T^3 - 1156*T^2 - 18764*T - 55203
$97$
\( T^{5} + 9 T^{4} - 48 T^{3} + \cdots + 3391 \)
T^5 + 9*T^4 - 48*T^3 - 429*T^2 + 555*T + 3391
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