[N,k,chi] = [16,16,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, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.1");
S:= CuspForms(chi, 16);
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 \(\beta = 640\sqrt{58}\).
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
\( T_{3}^{2} - 4072T_{3} - 19611504 \)
T3^2 - 4072*T3 - 19611504
acting on \(S_{16}^{\mathrm{new}}(\Gamma_0(16))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} - 4072 T - 19611504 \)
T^2 - 4072*T - 19611504
$5$
\( T^{2} + 140260 T - 25870595900 \)
T^2 + 140260*T - 25870595900
$7$
\( T^{2} + 126192 T - 188448974784 \)
T^2 + 126192*T - 188448974784
$11$
\( T^{2} + 20682632 T - 70\!\cdots\!44 \)
T^2 + 20682632*T - 7008984916431344
$13$
\( T^{2} - 499806476 T + 62\!\cdots\!44 \)
T^2 - 499806476*T + 62321545628804644
$17$
\( T^{2} - 3139516900 T + 17\!\cdots\!00 \)
T^2 - 3139516900*T + 1729120386527253700
$19$
\( T^{2} - 474668552 T - 18\!\cdots\!24 \)
T^2 - 474668552*T - 1884343362631895024
$23$
\( T^{2} - 40776002608 T + 41\!\cdots\!16 \)
T^2 - 40776002608*T + 411730471015105700416
$29$
\( T^{2} - 35253157356 T - 87\!\cdots\!16 \)
T^2 - 35253157356*T - 8724238988450049289116
$31$
\( T^{2} - 34389193280 T - 22\!\cdots\!00 \)
T^2 - 34389193280*T - 22260516977692033203200
$37$
\( T^{2} - 870228564444 T + 88\!\cdots\!84 \)
T^2 - 870228564444*T + 88000505814251052150084
$41$
\( T^{2} - 900085452084 T - 33\!\cdots\!36 \)
T^2 - 900085452084*T - 3306448549889071371545436
$43$
\( T^{2} + 500707998536 T - 33\!\cdots\!76 \)
T^2 + 500707998536*T - 3305933151930097687195376
$47$
\( T^{2} + 1208059119264 T - 26\!\cdots\!76 \)
T^2 + 1208059119264*T - 2648514116035900379563776
$53$
\( T^{2} - 1236734202044 T - 31\!\cdots\!16 \)
T^2 - 1236734202044*T - 31991791752008305595022716
$59$
\( T^{2} + 14441975905064 T + 33\!\cdots\!24 \)
T^2 + 14441975905064*T + 33550817901113315257703824
$61$
\( T^{2} - 18336303417260 T + 41\!\cdots\!00 \)
T^2 - 18336303417260*T + 41754812923193923687593700
$67$
\( T^{2} - 76601421514856 T - 13\!\cdots\!16 \)
T^2 - 76601421514856*T - 131386449482153213260060016
$71$
\( T^{2} - 145877173886864 T + 52\!\cdots\!24 \)
T^2 - 145877173886864*T + 5253050087176522873741839424
$73$
\( T^{2} + 26417269924108 T - 73\!\cdots\!84 \)
T^2 + 26417269924108*T - 7313348331336516083566737884
$79$
\( T^{2} + 257907833388128 T + 13\!\cdots\!96 \)
T^2 + 257907833388128*T + 13202697752495016635302103296
$83$
\( T^{2} + 255512806582648 T - 13\!\cdots\!24 \)
T^2 + 255512806582648*T - 13167165244609995987095754224
$89$
\( T^{2} + 719794611712812 T + 39\!\cdots\!36 \)
T^2 + 719794611712812*T + 39007101973745263138797528036
$97$
\( T^{2} - 407635590418756 T - 15\!\cdots\!16 \)
T^2 - 407635590418756*T - 1559707551282811639375616833916
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