[N,k,chi] = [20,10,Mod(1,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.1");
S:= CuspForms(chi, 10);
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
sage: f.q_expansion() # note that sage often uses an isomorphic number field
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 16\sqrt{79}\).
We also show the integral \(q\)-expansion of the trace form .
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
\(2\)
\(-1\)
\(5\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} + 260T_{3} - 3324 \)
T3^2 + 260*T3 - 3324
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(20))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} + 260T - 3324 \)
T^2 + 260*T - 3324
$5$
\( (T + 625)^{2} \)
(T + 625)^2
$7$
\( T^{2} + 380 T - 96250364 \)
T^2 + 380*T - 96250364
$11$
\( T^{2} - 102720 T + 2619648000 \)
T^2 - 102720*T + 2619648000
$13$
\( T^{2} - 179140 T + 1589611396 \)
T^2 - 179140*T + 1589611396
$17$
\( T^{2} - 316020 T + 22517952804 \)
T^2 - 316020*T + 22517952804
$19$
\( T^{2} - 137272 T - 533765233904 \)
T^2 - 137272*T - 533765233904
$23$
\( T^{2} + 665460 T - 715854707676 \)
T^2 + 665460*T - 715854707676
$29$
\( T^{2} + 6893748 T + 11181707706276 \)
T^2 + 6893748*T + 11181707706276
$31$
\( T^{2} - 291832 T - 13914308520944 \)
T^2 - 291832*T - 13914308520944
$37$
\( T^{2} - 11261380 T - 41043496652924 \)
T^2 - 11261380*T - 41043496652924
$41$
\( T^{2} + \cdots + 116248533661476 \)
T^2 - 29773452*T + 116248533661476
$43$
\( T^{2} + \cdots - 166415379974300 \)
T^2 + 11708180*T - 166415379974300
$47$
\( T^{2} + \cdots + 939697938528804 \)
T^2 - 62493300*T + 939697938528804
$53$
\( T^{2} + \cdots - 891341422077276 \)
T^2 - 9417780*T - 891341422077276
$59$
\( T^{2} + \cdots - 669513681826416 \)
T^2 + 92930856*T - 669513681826416
$61$
\( T^{2} + \cdots - 954028889496956 \)
T^2 - 195673924*T - 954028889496956
$67$
\( T^{2} + 219767420 T + 11\!\cdots\!96 \)
T^2 + 219767420*T + 11239877195400196
$71$
\( T^{2} - 311207016 T - 15\!\cdots\!36 \)
T^2 - 311207016*T - 15291364811604336
$73$
\( T^{2} + 99224060 T - 82\!\cdots\!44 \)
T^2 + 99224060*T - 82340726355330044
$79$
\( T^{2} - 542261776 T + 73\!\cdots\!44 \)
T^2 - 542261776*T + 73412804192378944
$83$
\( T^{2} + 1256915700 T + 39\!\cdots\!24 \)
T^2 + 1256915700*T + 394206281091180324
$89$
\( T^{2} + 462291852 T - 54\!\cdots\!24 \)
T^2 + 462291852*T - 541109639379720924
$97$
\( T^{2} - 1671716740 T + 52\!\cdots\!36 \)
T^2 - 1671716740*T + 528228461547839236
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