[N,k,chi] = [224,6,Mod(1,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.1");
S:= CuspForms(chi, 6);
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
\( p \)
Sign
\(2\)
\(-1\)
\(7\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{3} + 8T_{3}^{2} - 408T_{3} - 3096 \)
T3^3 + 8*T3^2 - 408*T3 - 3096
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(224))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( T^{3} + 8 T^{2} - 408 T - 3096 \)
T^3 + 8*T^2 - 408*T - 3096
$5$
\( T^{3} + 14 T^{2} - 4516 T - 129024 \)
T^3 + 14*T^2 - 4516*T - 129024
$7$
\( (T - 49)^{3} \)
(T - 49)^3
$11$
\( T^{3} + 600 T^{2} - 42560 T - 1824064 \)
T^3 + 600*T^2 - 42560*T - 1824064
$13$
\( T^{3} + 974 T^{2} + \cdots - 53052784 \)
T^3 + 974*T^2 - 243188*T - 53052784
$17$
\( T^{3} - 718 T^{2} + \cdots + 178338584 \)
T^3 - 718*T^2 - 286868*T + 178338584
$19$
\( T^{3} - 1056 T^{2} + \cdots + 936225400 \)
T^3 - 1056*T^2 - 3334760*T + 936225400
$23$
\( T^{3} - 3760 T^{2} + \cdots - 265872000 \)
T^3 - 3760*T^2 + 2021200*T - 265872000
$29$
\( T^{3} + 9134 T^{2} + \cdots + 18655265000 \)
T^3 + 9134*T^2 + 23616172*T + 18655265000
$31$
\( T^{3} + 1448 T^{2} + \cdots - 54502545600 \)
T^3 + 1448*T^2 - 46997056*T - 54502545600
$37$
\( T^{3} + 4998 T^{2} + \cdots + 417364199688 \)
T^3 + 4998*T^2 - 141204692*T + 417364199688
$41$
\( T^{3} + 23186 T^{2} + \cdots - 195051110440 \)
T^3 + 23186*T^2 + 107725644*T - 195051110440
$43$
\( T^{3} + 29880 T^{2} + \cdots + 302765738048 \)
T^3 + 29880*T^2 + 196212352*T + 302765738048
$47$
\( T^{3} - 10840 T^{2} + \cdots + 1468178593088 \)
T^3 - 10840*T^2 - 138708704*T + 1468178593088
$53$
\( T^{3} + 28006 T^{2} + \cdots - 1608716275704 \)
T^3 + 28006*T^2 - 273707828*T - 1608716275704
$59$
\( T^{3} - 17456 T^{2} + \cdots + 27263200844760 \)
T^3 - 17456*T^2 - 2364034264*T + 27263200844760
$61$
\( T^{3} + 92294 T^{2} + \cdots + 18497589110240 \)
T^3 + 92294*T^2 + 2524512604*T + 18497589110240
$67$
\( T^{3} + \cdots - 132723178706432 \)
T^3 + 56024*T^2 - 2493358576*T - 132723178706432
$71$
\( T^{3} - 77064 T^{2} + \cdots + 12186764730368 \)
T^3 - 77064*T^2 + 1117481920*T + 12186764730368
$73$
\( T^{3} + 46346 T^{2} + \cdots - 39799282328008 \)
T^3 + 46346*T^2 - 1534756916*T - 39799282328008
$79$
\( T^{3} + 4376 T^{2} + \cdots - 267561011200 \)
T^3 + 4376*T^2 - 427156800*T - 267561011200
$83$
\( T^{3} + \cdots - 109229539940808 \)
T^3 + 107128*T^2 - 162805672*T - 109229539940808
$89$
\( T^{3} - 29814 T^{2} + \cdots + 4144636813752 \)
T^3 - 29814*T^2 - 550096884*T + 4144636813752
$97$
\( T^{3} + \cdots - 698292640604904 \)
T^3 + 156482*T^2 - 4708729204*T - 698292640604904
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