[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 \(\beta = 3\sqrt{530401}\).
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
\( T_{2}^{2} - 1242T_{2} - 4387968 \)
T2^2 - 1242*T2 - 4387968
acting on \(S_{24}^{\mathrm{new}}(\Gamma_0(9))\).
$p$
$F_p(T)$
$2$
\( T^{2} - 1242 T - 4387968 \)
T^2 - 1242*T - 4387968
$3$
\( T^{2} \)
T^2
$5$
\( T^{2} - 46808820 T - 18\!\cdots\!00 \)
T^2 - 46808820*T - 18230649038977500
$7$
\( T^{2} + 211963904 T - 63\!\cdots\!80 \)
T^2 + 211963904*T - 63328399416459591680
$11$
\( T^{2} + 1468972366488 T + 45\!\cdots\!72 \)
T^2 + 1468972366488*T + 451328788810467841494672
$13$
\( T^{2} - 10491654264748 T + 19\!\cdots\!72 \)
T^2 - 10491654264748*T + 19433853389687863881209572
$17$
\( T^{2} - 210888011520828 T + 10\!\cdots\!96 \)
T^2 - 210888011520828*T + 10015857623742490931397291396
$19$
\( T^{2} + 907382448537944 T + 10\!\cdots\!80 \)
T^2 + 907382448537944*T + 108624979037988669753328366480
$23$
\( T^{2} + \cdots + 25\!\cdots\!60 \)
T^2 + 10116923323892112*T + 25525152797035773713066348420160
$29$
\( T^{2} + \cdots - 48\!\cdots\!40 \)
T^2 + 18478753545176892*T - 481110155158433604538295632226940
$31$
\( T^{2} + \cdots + 15\!\cdots\!00 \)
T^2 + 272793622592745488*T + 15545058952901236067836578079604800
$37$
\( T^{2} + 478995036787364 T - 14\!\cdots\!80 \)
T^2 + 478995036787364*T - 1426629656367456287643501711007195580
$41$
\( T^{2} + \cdots - 71\!\cdots\!20 \)
T^2 + 5555714961308771412*T - 7181632029129270875417381443518632220
$43$
\( T^{2} + \cdots - 99\!\cdots\!24 \)
T^2 + 1198322147609320040*T - 99946058339821534625730909593276231024
$47$
\( T^{2} + \cdots + 17\!\cdots\!44 \)
T^2 + 26308565672855777280*T + 170906042212863442389442360636906143744
$53$
\( T^{2} + \cdots - 26\!\cdots\!80 \)
T^2 - 41127501899415224628*T - 2615037447362584224885123771396070482780
$59$
\( T^{2} + \cdots + 11\!\cdots\!00 \)
T^2 - 307537061909444286696*T + 11144211555869809638822044735409640314000
$61$
\( T^{2} + \cdots + 38\!\cdots\!76 \)
T^2 - 594961179098503751020*T + 38813107730946228257095074595917951211876
$67$
\( T^{2} + \cdots + 43\!\cdots\!36 \)
T^2 + 1630225825126993264088*T + 433603634059432121997599539503367147432336
$71$
\( T^{2} + \cdots - 47\!\cdots\!56 \)
T^2 - 383942598581649272976*T - 4741312175779896881293717964129035521387456
$73$
\( T^{2} + \cdots - 66\!\cdots\!80 \)
T^2 + 2812202351440561692428*T - 666685506353955864075365469777029719164380
$79$
\( T^{2} + \cdots - 13\!\cdots\!00 \)
T^2 - 21069388575313284880*T - 133275564243622645369397613855250957092800
$83$
\( T^{2} + \cdots + 48\!\cdots\!68 \)
T^2 - 14817262080324402696024*T + 48172913975390379837054816774411522224020368
$89$
\( T^{2} + \cdots + 20\!\cdots\!80 \)
T^2 - 43449805260884456557164*T + 204175357299060740568865479893655861272487780
$97$
\( T^{2} + \cdots + 10\!\cdots\!16 \)
T^2 - 107136573045242168450692*T + 1066496513920101941686116577935158941895085316
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