[N,k,chi] = [9,24,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 24);
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 \(\beta = 12\sqrt{144169}\).
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
\( T_{2}^{2} + 1080T_{2} - 20468736 \)
T2^2 + 1080*T2 - 20468736
acting on \(S_{24}^{\mathrm{new}}(\Gamma_0(9))\).
$p$
$F_p(T)$
$2$
\( T^{2} + 1080 T - 20468736 \)
T^2 + 1080*T - 20468736
$3$
\( T^{2} \)
T^2
$5$
\( T^{2} + 73069020 T - 33\!\cdots\!00 \)
T^2 + 73069020*T - 3361250798797500
$7$
\( T^{2} + 1359184400 T - 19\!\cdots\!36 \)
T^2 + 1359184400*T - 19714065371291135936
$11$
\( T^{2} + 856801968264 T + 15\!\cdots\!24 \)
T^2 + 856801968264*T + 152480473377151271633424
$13$
\( T^{2} - 4376109322060 T - 28\!\cdots\!24 \)
T^2 - 4376109322060*T - 28609827010851645818437724
$17$
\( T^{2} + 254028147597540 T + 46\!\cdots\!64 \)
T^2 + 254028147597540*T + 4645977130345617355832980164
$19$
\( T^{2} - 4260600979960 T - 39\!\cdots\!00 \)
T^2 - 4260600979960*T - 390890637284318960442727766000
$23$
\( T^{2} + \cdots + 16\!\cdots\!96 \)
T^2 - 8144713079008560*T + 16349352142320793124704986348096
$29$
\( T^{2} + \cdots - 85\!\cdots\!00 \)
T^2 + 20818433601623340*T - 852741827545480891538082188521500
$31$
\( T^{2} + \cdots + 18\!\cdots\!64 \)
T^2 - 137714017177000384*T + 185013381333206480619537631396864
$37$
\( T^{2} + \cdots - 42\!\cdots\!36 \)
T^2 + 897721264408967780*T - 422811213787781995025683747721355836
$41$
\( T^{2} + \cdots - 51\!\cdots\!16 \)
T^2 - 2294435477168314956*T - 5175989760250467987484363287358119516
$43$
\( T^{2} + \cdots - 43\!\cdots\!64 \)
T^2 + 1750760768619855800*T - 430924970220552207758522075394804464
$47$
\( T^{2} + \cdots - 21\!\cdots\!36 \)
T^2 + 15759744217656780960*T - 212082722765888031552039011400776967936
$53$
\( T^{2} + \cdots + 48\!\cdots\!56 \)
T^2 - 140287253401646796420*T + 4881689282828580850774903446073665105156
$59$
\( T^{2} + \cdots - 28\!\cdots\!00 \)
T^2 + 280872989971340771880*T - 287141317524725751037029810398574438000
$61$
\( T^{2} + \cdots - 13\!\cdots\!76 \)
T^2 + 180452892516502223636*T - 134413668840629596265010008968606860734876
$67$
\( T^{2} + \cdots + 40\!\cdots\!64 \)
T^2 - 1754233163431557625240*T + 409680143490650218652123231451406645035664
$71$
\( T^{2} + \cdots + 17\!\cdots\!44 \)
T^2 + 3055033510194143328624*T + 1750877789068333226631930662727661614433344
$73$
\( T^{2} + \cdots + 15\!\cdots\!96 \)
T^2 + 8063408253877606149260*T + 15965868396225968204333434069799336092015396
$79$
\( T^{2} + \cdots - 40\!\cdots\!00 \)
T^2 - 6244916814559639980640*T - 40838059069801232593874766669935539561568000
$83$
\( T^{2} + \cdots - 11\!\cdots\!84 \)
T^2 + 6875994082418498976120*T - 112591047310494995468805854565351745122035184
$89$
\( T^{2} + \cdots + 82\!\cdots\!00 \)
T^2 + 6395093086173070004820*T + 8298778222734759129202752403913138041846500
$97$
\( T^{2} + \cdots - 93\!\cdots\!36 \)
T^2 + 31147288846254030500540*T - 9386917752510939863135558524811583300529914236
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