[N,k,chi] = [3,28,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, 28, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 28);
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 \(\beta = 144\sqrt{6469}\).
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
\( T_{2}^{2} - 3168T_{2} - 131632128 \)
T2^2 - 3168*T2 - 131632128
acting on \(S_{28}^{\mathrm{new}}(\Gamma_0(3))\).
$p$
$F_p(T)$
$2$
\( T^{2} - 3168 T - 131632128 \)
T^2 - 3168*T - 131632128
$3$
\( (T - 1594323)^{2} \)
(T - 1594323)^2
$5$
\( T^{2} + 4906065060 T + 85\!\cdots\!00 \)
T^2 + 4906065060*T + 851573139571282500
$7$
\( T^{2} + 151657089584 T - 64\!\cdots\!20 \)
T^2 + 151657089584*T - 64463449760079831043520
$11$
\( T^{2} - 40854992127048 T - 14\!\cdots\!08 \)
T^2 - 40854992127048*T - 14402975915786145256360340208
$13$
\( T^{2} + 417397898638292 T - 39\!\cdots\!88 \)
T^2 + 417397898638292*T - 393604601297227685583157327388
$17$
\( T^{2} + \cdots + 13\!\cdots\!16 \)
T^2 + 73795652103164508*T + 1361170048650162754352364902990916
$19$
\( T^{2} + \cdots + 90\!\cdots\!80 \)
T^2 + 346903482355728584*T + 9028616337125852668904416166225680
$23$
\( T^{2} + \cdots - 42\!\cdots\!60 \)
T^2 - 2497625277930684432*T - 421453513291603201243889590470836160
$29$
\( T^{2} + \cdots + 31\!\cdots\!20 \)
T^2 + 66866817822024885588*T + 315259978433741544652125884599789934820
$31$
\( T^{2} + \cdots - 42\!\cdots\!00 \)
T^2 + 131371412087557498208*T - 4254728371779122964832583815112666105600
$37$
\( T^{2} + \cdots - 23\!\cdots\!80 \)
T^2 + 247578887064220048004*T - 2392305853997411445252939027445154270755580
$41$
\( T^{2} + \cdots - 34\!\cdots\!40 \)
T^2 - 5075362465608343410612*T - 3461903388861245408199453214515725704104540
$43$
\( T^{2} + \cdots + 31\!\cdots\!76 \)
T^2 + 35862665467692465632120*T + 319139284780944393094331626115097901460636176
$47$
\( T^{2} + \cdots - 12\!\cdots\!36 \)
T^2 - 48518144960084941517280*T - 1206674298439992419504427670820297480074043136
$53$
\( T^{2} + \cdots + 30\!\cdots\!00 \)
T^2 - 350385928874194434085692*T + 30373762057065515409662418255967739546717453700
$59$
\( T^{2} + \cdots + 43\!\cdots\!20 \)
T^2 + 1574701087781292940777176*T + 437893143963063313825546736790672495798298834320
$61$
\( T^{2} + \cdots - 28\!\cdots\!44 \)
T^2 + 298583192683280602714100*T - 2891813523942130504551072665226300321635778682844
$67$
\( T^{2} + \cdots - 20\!\cdots\!64 \)
T^2 + 1451788236633679878778088*T - 203779446500095437448733775815456484204108766064
$71$
\( T^{2} + \cdots + 42\!\cdots\!44 \)
T^2 + 18927618367388181178813776*T + 42392760809205502845560390993579893637240415342144
$73$
\( T^{2} + \cdots - 68\!\cdots\!40 \)
T^2 + 18475598829856936295245388*T - 68772783934687967138031464834569059418239514203740
$79$
\( T^{2} + \cdots - 13\!\cdots\!00 \)
T^2 + 29951640885798459169010240*T - 1312710311974894869863820859825288512569330517785600
$83$
\( T^{2} + \cdots + 13\!\cdots\!68 \)
T^2 - 68977464913739379133962936*T + 137191680765197663399426908093852830029065033578768
$89$
\( T^{2} + \cdots + 61\!\cdots\!40 \)
T^2 - 525251854986446192504396436*T + 61609925451808023502199386153110863305750186959837540
$97$
\( T^{2} + \cdots - 18\!\cdots\!64 \)
T^2 - 792881154632193034514966212*T - 189680116880513317769263292124678934263440487932055164
show more
show less