[N,k,chi] = [18,40,Mod(1,18)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(18, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 40, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("18.1");
S:= CuspForms(chi, 40);
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 \(\beta = 673920\sqrt{12925296409}\).
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
\(2\)
\(-1\)
\(3\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{2} + 6873268566540T_{5} - 2266606978164805175391937500 \)
T5^2 + 6873268566540*T5 - 2266606978164805175391937500
acting on \(S_{40}^{\mathrm{new}}(\Gamma_0(18))\).
$p$
$F_p(T)$
$2$
\( (T - 524288)^{2} \)
(T - 524288)^2
$3$
\( T^{2} \)
T^2
$5$
\( T^{2} + 6873268566540 T - 22\!\cdots\!00 \)
T^2 + 6873268566540*T - 2266606978164805175391937500
$7$
\( T^{2} + \cdots - 74\!\cdots\!64 \)
T^2 - 12892539328650112*T - 749350429041674598666275392139264
$11$
\( T^{2} + \cdots + 83\!\cdots\!64 \)
T^2 + 338694700199233311384*T + 8310518665590408100201242396397182021264
$13$
\( T^{2} + \cdots - 53\!\cdots\!16 \)
T^2 - 4612486018762882054444*T - 53840589511458284943493787976430601300236316
$17$
\( T^{2} + \cdots + 40\!\cdots\!16 \)
T^2 + 1274685078144611712164292*T + 404114245839588099994525834542481592325911971716
$19$
\( T^{2} + \cdots - 56\!\cdots\!00 \)
T^2 + 7871163188560387995242840*T - 56184655571239174908705192964318128528401904422000
$23$
\( T^{2} + \cdots + 17\!\cdots\!44 \)
T^2 - 928698621489419035155025776*T + 175911576826110140270364186642793180993931328289018944
$29$
\( T^{2} + \cdots - 26\!\cdots\!00 \)
T^2 + 3222882338181375779334996540*T - 2651165143696222173654001970570559543376840474687979749500
$31$
\( T^{2} + \cdots - 12\!\cdots\!16 \)
T^2 + 109189404560424435417169383056*T - 12340926457816308974504576946898205788902106351546036730816
$37$
\( T^{2} + \cdots + 41\!\cdots\!76 \)
T^2 + 2966497020246826634428217530148*T + 414034774942326871074447788244158208284151018015518308491076
$41$
\( T^{2} + \cdots - 21\!\cdots\!56 \)
T^2 - 3184130919919450005449131138476*T - 214479581071749941604648568816218382224296967265675924959388956
$43$
\( T^{2} + \cdots + 35\!\cdots\!64 \)
T^2 - 121276829032728092851660993087384*T + 3528427139172420535392502275395560449585267499673308004164856464
$47$
\( T^{2} + \cdots - 15\!\cdots\!44 \)
T^2 + 167353337359718168352138616780032*T - 15640249131454023812558368981354894461262330832104354539026694144
$53$
\( T^{2} + \cdots - 27\!\cdots\!76 \)
T^2 - 849638757758267013248051927600436*T - 27013236340298570993792718506177252387810160238998347672617465686876
$59$
\( T^{2} + \cdots + 38\!\cdots\!00 \)
T^2 + 57757426692930616282381230017427480*T + 380349182540104710564432187810489339460522680075279730271010913427600
$61$
\( T^{2} + \cdots + 41\!\cdots\!64 \)
T^2 - 139585870546791326724837331931195884*T + 4108457088370485867427337591769720002927814253645103291972525356145764
$67$
\( T^{2} + \cdots + 23\!\cdots\!16 \)
T^2 - 787890812726209261623851169549764392*T + 23557359297557533269678409016992412112524431933849197499411784220528016
$71$
\( T^{2} + \cdots + 23\!\cdots\!24 \)
T^2 + 1031707278690747392271908420025354864*T + 239258498208841907781942164972891370243309581267616583103687456414121024
$73$
\( T^{2} + \cdots - 10\!\cdots\!56 \)
T^2 + 1320037261203960461831511534844081676*T - 10819913480718496551294454335867795668854378463208006388762187576302779356
$79$
\( T^{2} + \cdots + 14\!\cdots\!00 \)
T^2 - 25396887059925205007053002590900778640*T + 149106643708408772935704021223487983034456925318339435333389299588739368000
$83$
\( T^{2} + \cdots + 51\!\cdots\!04 \)
T^2 - 15439788347682410178859966268035620696*T + 51423623025180698639820750296150921280533180732271518722381368506581359504
$89$
\( T^{2} + \cdots + 13\!\cdots\!00 \)
T^2 - 241773033631135585334326710863937391980*T + 13701704785441218535842785809121369984937953466210085754243186838538428320100
$97$
\( T^{2} + \cdots - 35\!\cdots\!44 \)
T^2 - 144853232141161072344566878753620889732*T - 35354828454807676223057228097829508248914781661483393482884357765029492936444
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