[N,k,chi] = [93,4,Mod(1,93)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(93, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("93.1");
S:= CuspForms(chi, 4);
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 \(\beta = \frac{1}{2}(1 + \sqrt{41})\).
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
\(3\)
\(1\)
\(31\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{2} + T_{2} - 10 \)
T2^2 + T2 - 10
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(93))\).
$p$
$F_p(T)$
$2$
\( T^{2} + T - 10 \)
T^2 + T - 10
$3$
\( (T + 3)^{2} \)
(T + 3)^2
$5$
\( T^{2} + 11T - 62 \)
T^2 + 11*T - 62
$7$
\( T^{2} - 29T + 200 \)
T^2 - 29*T + 200
$11$
\( (T + 68)^{2} \)
(T + 68)^2
$13$
\( T^{2} + 20T - 2524 \)
T^2 + 20*T - 2524
$17$
\( T^{2} + 30T - 4736 \)
T^2 + 30*T - 4736
$19$
\( T^{2} - 117T + 460 \)
T^2 - 117*T + 460
$23$
\( T^{2} + 142T - 13040 \)
T^2 + 142*T - 13040
$29$
\( T^{2} - 74T - 5560 \)
T^2 - 74*T - 5560
$31$
\( (T - 31)^{2} \)
(T - 31)^2
$37$
\( T^{2} + 166T + 6520 \)
T^2 + 166*T + 6520
$41$
\( T^{2} + 161T - 106526 \)
T^2 + 161*T - 106526
$43$
\( T^{2} + 272T + 17840 \)
T^2 + 272*T + 17840
$47$
\( T^{2} + 680T + 114944 \)
T^2 + 680*T + 114944
$53$
\( T^{2} + 390T - 146024 \)
T^2 + 390*T - 146024
$59$
\( T^{2} + 363T - 476780 \)
T^2 + 363*T - 476780
$61$
\( T^{2} + 690T + 112096 \)
T^2 + 690*T + 112096
$67$
\( T^{2} - 256T - 272912 \)
T^2 - 256*T - 272912
$71$
\( T^{2} - 605T - 174184 \)
T^2 - 605*T - 174184
$73$
\( T^{2} - 578T + 49040 \)
T^2 - 578*T + 49040
$79$
\( T^{2} + 1030 T + 256000 \)
T^2 + 1030*T + 256000
$83$
\( T^{2} + 2046 T + 1007128 \)
T^2 + 2046*T + 1007128
$89$
\( T^{2} - 788T - 222620 \)
T^2 - 788*T - 222620
$97$
\( T^{2} - 1627 T + 333362 \)
T^2 - 1627*T + 333362
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