[N,k,chi] = [2,34,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 34);
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 \(\beta = 10560\sqrt{79829689}\).
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
\(2\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} - 8356488T_{3} - 8884638284346864 \)
T3^2 - 8356488*T3 - 8884638284346864
acting on \(S_{34}^{\mathrm{new}}(\Gamma_0(2))\).
$p$
$F_p(T)$
$2$
\( (T - 65536)^{2} \)
(T - 65536)^2
$3$
\( T^{2} - 8356488 T - 88\!\cdots\!64 \)
T^2 - 8356488*T - 8884638284346864
$5$
\( T^{2} + 5332476660 T - 14\!\cdots\!00 \)
T^2 + 5332476660*T - 142141702650797502337500
$7$
\( T^{2} - 132719095875856 T - 27\!\cdots\!16 \)
T^2 - 132719095875856*T - 2746952718235672201802004416
$11$
\( T^{2} + \cdots - 37\!\cdots\!56 \)
T^2 + 158105471422723176*T - 37365375247240412381507121493439856
$13$
\( T^{2} + \cdots + 45\!\cdots\!36 \)
T^2 - 4983398515499093788*T + 4562712760820196095509222354524541636
$17$
\( T^{2} + \cdots + 16\!\cdots\!44 \)
T^2 - 302465632526578851876*T + 16687799606513204486913558895834366034244
$19$
\( T^{2} + \cdots - 44\!\cdots\!00 \)
T^2 - 2235591200465928697000*T - 443509913730300228945806047270087490495600
$23$
\( T^{2} + \cdots + 12\!\cdots\!76 \)
T^2 + 71424561765127117190352*T + 1239890041422222361637698214321859418109184576
$29$
\( T^{2} + \cdots - 94\!\cdots\!00 \)
T^2 + 252883963720400854222020*T - 947948657921543071150167875944708097900864754300
$31$
\( T^{2} + \cdots + 46\!\cdots\!04 \)
T^2 + 4320085941116207893109696*T + 4623153038373856122534292113056059583179436360704
$37$
\( T^{2} + \cdots - 10\!\cdots\!56 \)
T^2 - 116026284407242232995257676*T - 1055014473182037735971351966366991249381370882059356
$41$
\( T^{2} + \cdots - 22\!\cdots\!56 \)
T^2 + 166777326610314677606684076*T - 221050065294573690675082811608071186359434402528924956
$43$
\( T^{2} + \cdots - 52\!\cdots\!24 \)
T^2 + 36726176847118764316966952*T - 5298166842071898453778859956770845330164505531879024
$47$
\( T^{2} + \cdots - 84\!\cdots\!16 \)
T^2 - 2869532951474224704935093856*T - 844718392025130708695339441893133778083915114172700416
$53$
\( T^{2} + \cdots + 33\!\cdots\!16 \)
T^2 + 4397747242775062628314771092*T + 3353757807655806091494107994109792561116489366477660516
$59$
\( T^{2} + \cdots - 12\!\cdots\!00 \)
T^2 - 187586852967550885385845088760*T - 12407351427860802977898023941174042079328088370541056137200
$61$
\( T^{2} + \cdots + 52\!\cdots\!04 \)
T^2 - 464465778169397582356016167804*T + 52353932069405220535539457672625613814462726636077513120004
$67$
\( T^{2} + \cdots + 13\!\cdots\!24 \)
T^2 + 749458286997747528573119702264*T + 131809700750196988167439795701130872296932904165437702315024
$71$
\( T^{2} + \cdots - 74\!\cdots\!76 \)
T^2 - 2607453085577305255019451429264*T - 7421912704365312646450388610794924936352309815783631541642176
$73$
\( T^{2} + \cdots + 63\!\cdots\!56 \)
T^2 + 5204971716349166463517155924332*T + 6330009395185254627354052428552168292979457898851892638617956
$79$
\( T^{2} + \cdots + 14\!\cdots\!00 \)
T^2 + 26559519161049342541312928970080*T + 148816983537766786898830969540678746722498450974447428095392000
$83$
\( T^{2} + \cdots - 75\!\cdots\!84 \)
T^2 + 37062506185061977386465584779992*T - 758542635515222209047304220976023020102417193833140970729359984
$89$
\( T^{2} + \cdots + 20\!\cdots\!00 \)
T^2 - 302974646079669442176749711731380*T + 20706175764425858460549861743188187444543015132192738931212936100
$97$
\( T^{2} + \cdots - 50\!\cdots\!36 \)
T^2 - 68100314316598271221487860024516*T - 50395544532073159442312597863551871749379147239875595434589901436
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