[N,k,chi] = [16,14,Mod(1,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.1");
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 \(\beta = 64\sqrt{781}\).
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
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} + 872T_{3} - 3008880 \)
T3^2 + 872*T3 - 3008880
acting on \(S_{14}^{\mathrm{new}}(\Gamma_0(16))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} + 872 T - 3008880 \)
T^2 + 872*T - 3008880
$5$
\( T^{2} - 18476 T - 375311900 \)
T^2 - 18476*T - 375311900
$7$
\( T^{2} + 110928 T - 154582077888 \)
T^2 + 110928*T - 154582077888
$11$
\( T^{2} + 16474040 T + 66946512008464 \)
T^2 + 16474040*T + 66946512008464
$13$
\( T^{2} + \cdots - 261630161766908 \)
T^2 - 18744572*T - 261630161766908
$17$
\( T^{2} + 153793628 T + 12\!\cdots\!40 \)
T^2 + 153793628*T + 1248955874435140
$19$
\( T^{2} - 118747640 T - 24\!\cdots\!36 \)
T^2 - 118747640*T - 24632151480932336
$23$
\( T^{2} + 718268912 T + 89\!\cdots\!92 \)
T^2 + 718268912*T + 89234191613718592
$29$
\( T^{2} - 309341340 T - 18\!\cdots\!44 \)
T^2 - 309341340*T - 18017079758784528444
$31$
\( T^{2} + 5767504192 T + 12\!\cdots\!20 \)
T^2 + 5767504192*T + 1281160652437611520
$37$
\( T^{2} + 11621553300 T - 30\!\cdots\!56 \)
T^2 + 11621553300*T - 302072630114754470556
$41$
\( T^{2} - 1311168276 T - 20\!\cdots\!12 \)
T^2 - 1311168276*T - 208379308896179149212
$43$
\( T^{2} - 29595620104 T - 60\!\cdots\!12 \)
T^2 - 29595620104*T - 60075724254670537712
$47$
\( T^{2} + 12313617888 T - 79\!\cdots\!64 \)
T^2 + 12313617888*T - 795791262951260446464
$53$
\( T^{2} + 38006007028 T - 79\!\cdots\!04 \)
T^2 + 38006007028*T - 7903309686498031869404
$59$
\( T^{2} + 253345911704 T - 43\!\cdots\!52 \)
T^2 + 253345911704*T - 43966963779441194947952
$61$
\( T^{2} + 647244384292 T + 10\!\cdots\!00 \)
T^2 + 647244384292*T + 104090815915098409701700
$67$
\( T^{2} + 1619993806312 T + 65\!\cdots\!12 \)
T^2 + 1619993806312*T + 651760213234629667514512
$71$
\( T^{2} - 1040270142512 T - 12\!\cdots\!40 \)
T^2 - 1040270142512*T - 127425734386880299605440
$73$
\( T^{2} - 4005283908692 T + 39\!\cdots\!52 \)
T^2 - 4005283908692*T + 3986855052624686801780452
$79$
\( T^{2} - 2521777572064 T + 70\!\cdots\!80 \)
T^2 - 2521777572064*T + 706372615385786681831680
$83$
\( T^{2} - 290486230904 T - 31\!\cdots\!72 \)
T^2 - 290486230904*T - 3155486939374437821234672
$89$
\( T^{2} + 8723755657740 T + 17\!\cdots\!04 \)
T^2 + 8723755657740*T + 17718204727961930852564004
$97$
\( T^{2} - 9601712299972 T - 53\!\cdots\!04 \)
T^2 - 9601712299972*T - 53188748503141922392161404
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