[N,k,chi] = [14,14,Mod(1,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14.1");
S:= CuspForms(chi, 14);
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 \(\beta = 2\sqrt{100129}\).
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
\(2\)
\(1\)
\(7\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} - 952T_{3} - 173940 \)
T3^2 - 952*T3 - 173940
acting on \(S_{14}^{\mathrm{new}}(\Gamma_0(14))\).
$p$
$F_p(T)$
$2$
\( (T + 64)^{2} \)
(T + 64)^2
$3$
\( T^{2} - 952T - 173940 \)
T^2 - 952*T - 173940
$5$
\( T^{2} - 32004 T - 1333584000 \)
T^2 - 32004*T - 1333584000
$7$
\( (T - 117649)^{2} \)
(T - 117649)^2
$11$
\( T^{2} + 1352736 T - 48783462900480 \)
T^2 + 1352736*T - 48783462900480
$13$
\( T^{2} - 3510388 T - 10\!\cdots\!64 \)
T^2 - 3510388*T - 1034376299351264
$17$
\( T^{2} - 217711956 T + 52\!\cdots\!48 \)
T^2 - 217711956*T + 5258212862273748
$19$
\( T^{2} - 591335752 T + 82\!\cdots\!20 \)
T^2 - 591335752*T + 82202600320772620
$23$
\( T^{2} - 840735000 T - 30\!\cdots\!00 \)
T^2 - 840735000*T - 307342956281760000
$29$
\( T^{2} + 487623540 T - 22\!\cdots\!36 \)
T^2 + 487623540*T - 2226593776636211436
$31$
\( T^{2} - 2193076144 T - 37\!\cdots\!32 \)
T^2 - 2193076144*T - 3721530883884270032
$37$
\( T^{2} - 405060268 T - 38\!\cdots\!20 \)
T^2 - 405060268*T - 38874132892883083820
$41$
\( T^{2} - 8518172628 T - 10\!\cdots\!08 \)
T^2 - 8518172628*T - 1059067594010925144108
$43$
\( T^{2} - 26225045296 T - 36\!\cdots\!32 \)
T^2 - 26225045296*T - 361109483047367824832
$47$
\( T^{2} - 155048849760 T + 57\!\cdots\!76 \)
T^2 - 155048849760*T + 5792760019303470702576
$53$
\( T^{2} - 66007050492 T - 45\!\cdots\!08 \)
T^2 - 66007050492*T - 45166821633697705218108
$59$
\( T^{2} + 476362296984 T + 36\!\cdots\!68 \)
T^2 + 476362296984*T + 36328882653143886015468
$61$
\( T^{2} - 197378850004 T - 54\!\cdots\!12 \)
T^2 - 197378850004*T - 54835042895671583009312
$67$
\( T^{2} + 1718732859488 T + 45\!\cdots\!92 \)
T^2 + 1718732859488*T + 455695737272632691978992
$71$
\( T^{2} + 695543478336 T - 12\!\cdots\!60 \)
T^2 + 695543478336*T - 1210980536457371281244160
$73$
\( T^{2} + 466085239340 T - 76\!\cdots\!84 \)
T^2 + 466085239340*T - 764431721640675397512284
$79$
\( T^{2} + 2432016575840 T - 11\!\cdots\!04 \)
T^2 + 2432016575840*T - 1119754406216115236343104
$83$
\( T^{2} + 1743984494616 T - 26\!\cdots\!32 \)
T^2 + 1743984494616*T - 265919305746777140038932
$89$
\( T^{2} - 3022580240484 T - 21\!\cdots\!20 \)
T^2 - 3022580240484*T - 21341031593067258922620
$97$
\( T^{2} - 7760062661092 T + 68\!\cdots\!60 \)
T^2 - 7760062661092*T + 6875529282397745680372660
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