[N,k,chi] = [3,18,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 18);
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 \(\beta = 3\sqrt{14569}\).
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
\(3\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{2} - 594T_{2} - 42912 \)
T2^2 - 594*T2 - 42912
acting on \(S_{18}^{\mathrm{new}}(\Gamma_0(3))\).
$p$
$F_p(T)$
$2$
\( T^{2} - 594T - 42912 \)
T^2 - 594*T - 42912
$3$
\( (T - 6561)^{2} \)
(T - 6561)^2
$5$
\( T^{2} - 382860 T - 1587996193500 \)
T^2 - 382860*T - 1587996193500
$7$
\( T^{2} - 24471568 T + 36563624964160 \)
T^2 - 24471568*T + 36563624964160
$11$
\( T^{2} + 987553512 T + 24\!\cdots\!72 \)
T^2 + 987553512*T + 241662899580669072
$13$
\( T^{2} + 2519398244 T + 85\!\cdots\!88 \)
T^2 + 2519398244*T + 85826630199297988
$17$
\( T^{2} + 34313126364 T + 23\!\cdots\!24 \)
T^2 + 34313126364*T + 234781594617081830724
$19$
\( T^{2} - 80053542184 T - 18\!\cdots\!20 \)
T^2 - 80053542184*T - 185234520277889694320
$23$
\( T^{2} - 297228742704 T - 22\!\cdots\!20 \)
T^2 - 297228742704*T - 222412635685819130166720
$29$
\( T^{2} + 470374069572 T - 50\!\cdots\!80 \)
T^2 + 470374069572*T - 502734177663602624512380
$31$
\( T^{2} - 3400754454592 T + 37\!\cdots\!00 \)
T^2 - 3400754454592*T + 376073386682108523443200
$37$
\( T^{2} - 10652012180428 T - 41\!\cdots\!20 \)
T^2 - 10652012180428*T - 413610177451119192548099420
$41$
\( T^{2} + 113376799448748 T + 26\!\cdots\!40 \)
T^2 + 113376799448748*T + 2666589765699308594999488740
$43$
\( T^{2} - 61637031489880 T - 36\!\cdots\!96 \)
T^2 - 61637031489880*T - 3605412239982138048161680496
$47$
\( T^{2} + 279645641926560 T + 19\!\cdots\!36 \)
T^2 + 279645641926560*T + 19055553710579005582938491136
$53$
\( T^{2} + 530964038611476 T + 54\!\cdots\!20 \)
T^2 + 530964038611476*T + 54965175144381085457532216420
$59$
\( T^{2} + \cdots - 17\!\cdots\!80 \)
T^2 - 1727524231086456*T - 179080275397350121743603037680
$61$
\( T^{2} + \cdots + 19\!\cdots\!56 \)
T^2 - 2784287656027900*T + 1937726483198503748375663473156
$67$
\( T^{2} + \cdots + 27\!\cdots\!64 \)
T^2 + 3329301676696184*T + 2733616113184466986354889000464
$71$
\( T^{2} + \cdots + 45\!\cdots\!64 \)
T^2 + 13489402206504816*T + 45166429353916529613725667660864
$73$
\( T^{2} - 436589918136724 T - 17\!\cdots\!00 \)
T^2 - 436589918136724*T - 175242316299457817977086373843100
$79$
\( T^{2} + \cdots - 10\!\cdots\!00 \)
T^2 - 4376041565214880*T - 106848883990011720062065941804800
$83$
\( T^{2} + \cdots + 36\!\cdots\!72 \)
T^2 + 39886442265612888*T + 365757457501467273571999574646672
$89$
\( T^{2} + \cdots - 16\!\cdots\!60 \)
T^2 - 6972184096107444*T - 1690885178941200888313319251706460
$97$
\( T^{2} + \cdots + 81\!\cdots\!04 \)
T^2 - 183569555712460996*T + 8114017702591983179536147275888004
show more
show less