[N,k,chi] = [27,10,Mod(1,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.1");
S:= CuspForms(chi, 10);
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
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
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} - 3T_{2}^{2} - 1062T_{2} + 3672 \)
T2^3 - 3*T2^2 - 1062*T2 + 3672
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(27))\).
$p$
$F_p(T)$
$2$
\( T^{3} - 3 T^{2} - 1062 T + 3672 \)
T^3 - 3*T^2 - 1062*T + 3672
$3$
\( T^{3} \)
T^3
$5$
\( T^{3} + 1983 T^{2} + \cdots - 3825897975 \)
T^3 + 1983*T^2 - 2030409*T - 3825897975
$7$
\( T^{3} + 3693 T^{2} + \cdots + 90362069875 \)
T^3 + 3693*T^2 - 63178017*T + 90362069875
$11$
\( T^{3} + 16863 T^{2} + \cdots + 30446445345165 \)
T^3 + 16863*T^2 - 2495944917*T + 30446445345165
$13$
\( T^{3} + \cdots + 955953747392320 \)
T^3 - 116916*T^2 - 16773786384*T + 955953747392320
$17$
\( T^{3} + 1014048 T^{2} + \cdots + 78\!\cdots\!84 \)
T^3 + 1014048*T^2 + 262405282752*T + 7875363087120384
$19$
\( T^{3} + 15222 T^{2} + \cdots + 44\!\cdots\!64 \)
T^3 + 15222*T^2 - 599886952548*T + 4462994708562664
$23$
\( T^{3} + 2927118 T^{2} + \cdots - 45\!\cdots\!72 \)
T^3 + 2927118*T^2 - 934856229204*T - 4569487178132998872
$29$
\( T^{3} + 5768790 T^{2} + \cdots - 42\!\cdots\!80 \)
T^3 + 5768790*T^2 + 3737351821212*T - 4293003942319875480
$31$
\( T^{3} + 6575223 T^{2} + \cdots - 62\!\cdots\!31 \)
T^3 + 6575223*T^2 - 17750049491193*T - 62492650240019533631
$37$
\( T^{3} + 11686026 T^{2} + \cdots - 10\!\cdots\!80 \)
T^3 + 11686026*T^2 - 88280093334516*T - 1047077879527633361480
$41$
\( T^{3} - 22213518 T^{2} + \cdots + 36\!\cdots\!80 \)
T^3 - 22213518*T^2 - 126697103716932*T + 3654362317389671607480
$43$
\( T^{3} - 45384414 T^{2} + \cdots + 45\!\cdots\!60 \)
T^3 - 45384414*T^2 - 922994517755364*T + 45693288572826916191160
$47$
\( T^{3} + 12392034 T^{2} + \cdots - 10\!\cdots\!60 \)
T^3 + 12392034*T^2 - 665782616655828*T - 10277791691826528605160
$53$
\( T^{3} + 80579637 T^{2} + \cdots - 13\!\cdots\!97 \)
T^3 + 80579637*T^2 - 969165886601457*T - 132145602899448674029797
$59$
\( T^{3} + 244026660 T^{2} + \cdots - 52\!\cdots\!40 \)
T^3 + 244026660*T^2 + 10798794175553712*T - 529092626093627389957440
$61$
\( T^{3} - 369729960 T^{2} + \cdots - 11\!\cdots\!48 \)
T^3 - 369729960*T^2 + 40441106001326016*T - 1155782701281291575694848
$67$
\( T^{3} + 252614586 T^{2} + \cdots - 19\!\cdots\!00 \)
T^3 + 252614586*T^2 + 2341428465809532*T - 1913537792585824549505000
$71$
\( T^{3} + 403193088 T^{2} + \cdots - 98\!\cdots\!40 \)
T^3 + 403193088*T^2 + 31952365891662528*T - 983330358019649001584640
$73$
\( T^{3} + 406626717 T^{2} + \cdots - 64\!\cdots\!45 \)
T^3 + 406626717*T^2 + 35133728293146243*T - 649410779968170038515745
$79$
\( T^{3} - 265451856 T^{2} + \cdots + 83\!\cdots\!08 \)
T^3 - 265451856*T^2 - 167392077475454016*T + 8342441668663075578999808
$83$
\( T^{3} + 121625871 T^{2} + \cdots - 21\!\cdots\!07 \)
T^3 + 121625871*T^2 - 39129315214744053*T - 2140703035426209727264707
$89$
\( T^{3} + 377904006 T^{2} + \cdots + 10\!\cdots\!00 \)
T^3 + 377904006*T^2 - 715058944722112068*T + 100155402365630652917073000
$97$
\( T^{3} + 438907539 T^{2} + \cdots - 26\!\cdots\!55 \)
T^3 + 438907539*T^2 - 130939166593400541*T - 26018968522107461502988655
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