[N,k,chi] = [4020,2,Mod(1,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4020.1");
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
\(2\)
\(-1\)
\(3\)
\(-1\)
\(5\)
\(1\)
\(67\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{7}^{6} - 3T_{7}^{5} - 18T_{7}^{4} + 60T_{7}^{3} + 51T_{7}^{2} - 264T_{7} + 176 \)
T7^6 - 3*T7^5 - 18*T7^4 + 60*T7^3 + 51*T7^2 - 264*T7 + 176
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4020))\).
$p$
$F_p(T)$
$2$
\( T^{6} \)
T^6
$3$
\( (T - 1)^{6} \)
(T - 1)^6
$5$
\( (T + 1)^{6} \)
(T + 1)^6
$7$
\( T^{6} - 3 T^{5} - 18 T^{4} + 60 T^{3} + \cdots + 176 \)
T^6 - 3*T^5 - 18*T^4 + 60*T^3 + 51*T^2 - 264*T + 176
$11$
\( T^{6} - 3 T^{5} - 36 T^{4} + 90 T^{3} + \cdots + 72 \)
T^6 - 3*T^5 - 36*T^4 + 90*T^3 + 117*T^2 - 216*T + 72
$13$
\( T^{6} - 3 T^{5} - 39 T^{4} + 119 T^{3} + \cdots + 46 \)
T^6 - 3*T^5 - 39*T^4 + 119*T^3 + 141*T^2 - 210*T + 46
$17$
\( T^{6} - 6 T^{5} - 24 T^{4} + 125 T^{3} + \cdots - 30 \)
T^6 - 6*T^5 - 24*T^4 + 125*T^3 + 21*T^2 - 162*T - 30
$19$
\( T^{6} + 3 T^{5} - 33 T^{4} - 27 T^{3} + \cdots - 64 \)
T^6 + 3*T^5 - 33*T^4 - 27*T^3 + 153*T^2 + 48*T - 64
$23$
\( T^{6} - 6 T^{5} - 60 T^{4} + \cdots - 2640 \)
T^6 - 6*T^5 - 60*T^4 + 254*T^3 + 939*T^2 - 2376*T - 2640
$29$
\( T^{6} - 21 T^{5} + 75 T^{4} + \cdots + 21516 \)
T^6 - 21*T^5 + 75*T^4 + 937*T^3 - 6549*T^2 + 4752*T + 21516
$31$
\( T^{6} + 3 T^{5} - 72 T^{4} + \cdots + 3370 \)
T^6 + 3*T^5 - 72*T^4 - 256*T^3 + 1155*T^2 + 5076*T + 3370
$37$
\( T^{6} - 102 T^{4} - 180 T^{3} + \cdots + 9476 \)
T^6 - 102*T^4 - 180*T^3 + 2505*T^2 + 9756*T + 9476
$41$
\( T^{6} - 9 T^{5} - 60 T^{4} + 424 T^{3} + \cdots - 960 \)
T^6 - 9*T^5 - 60*T^4 + 424*T^3 + 753*T^2 - 3024*T - 960
$43$
\( T^{6} + 3 T^{5} - 168 T^{4} + \cdots - 6040 \)
T^6 + 3*T^5 - 168*T^4 - 36*T^3 + 7263*T^2 - 16224*T - 6040
$47$
\( T^{6} - 21 T^{5} + 21 T^{4} + \cdots + 119256 \)
T^6 - 21*T^5 + 21*T^4 + 1891*T^3 - 9609*T^2 - 15984*T + 119256
$53$
\( T^{6} - 15 T^{5} - 171 T^{4} + \cdots + 287100 \)
T^6 - 15*T^5 - 171*T^4 + 2955*T^3 + 2583*T^2 - 125928*T + 287100
$59$
\( T^{6} - 15 T^{5} - 9 T^{4} + \cdots + 18198 \)
T^6 - 15*T^5 - 9*T^4 + 933*T^3 - 3105*T^2 - 3726*T + 18198
$61$
\( T^{6} - 15 T^{5} - 33 T^{4} + \cdots + 25524 \)
T^6 - 15*T^5 - 33*T^4 + 1009*T^3 - 1395*T^2 - 13392*T + 25524
$67$
\( (T - 1)^{6} \)
(T - 1)^6
$71$
\( T^{6} - 18 T^{5} - 126 T^{4} + \cdots + 473094 \)
T^6 - 18*T^5 - 126*T^4 + 3333*T^3 - 5319*T^2 - 124362*T + 473094
$73$
\( T^{6} + 6 T^{5} - 210 T^{4} + \cdots - 108284 \)
T^6 + 6*T^5 - 210*T^4 - 481*T^3 + 9501*T^2 + 11616*T - 108284
$79$
\( T^{6} - 9 T^{5} - 390 T^{4} + \cdots - 76530 \)
T^6 - 9*T^5 - 390*T^4 + 2554*T^3 + 31653*T^2 - 16272*T - 76530
$83$
\( T^{6} - 24 T^{5} + 210 T^{4} + \cdots - 360 \)
T^6 - 24*T^5 + 210*T^4 - 809*T^3 + 1215*T^2 - 144*T - 360
$89$
\( T^{6} - 24 T^{5} - 258 T^{4} + \cdots + 1927500 \)
T^6 - 24*T^5 - 258*T^4 + 9467*T^3 - 31983*T^2 - 453024*T + 1927500
$97$
\( T^{6} - 9 T^{5} - 129 T^{4} + \cdots - 13450 \)
T^6 - 9*T^5 - 129*T^4 + 1977*T^3 - 9339*T^2 + 18666*T - 13450
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