Embedded newform 189.2.v.a.43.2

• Label: 189.2.v.a.43.2
• Level: $189$
• Weight: $2$
• Character: 189.43
• Analytic conductor: $1.509$
• Analytic rank: $0$
• Dimension: $54$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.v (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.50917259820\)
Analytic rank:	\(0\)
Dimension:	\(54\)
Relative dimension:	\(9\) over \(\Q(\zeta_{9})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.2
Character	\(\chi\)	\(=\)	189.43
Dual form			189.2.v.a.22.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.17963 - 0.989828i) q^{2} +(0.853595 - 1.50711i) q^{3} +(0.0644735 + 0.365648i) q^{4} +(-1.99174 - 0.724932i) q^{5} +(-2.49871 + 0.932919i) q^{6} +(0.173648 - 0.984808i) q^{7} +(-1.25403 + 2.17204i) q^{8} +(-1.54275 - 2.57292i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\)	\(29\)	\(136\)
\(\chi(n)\)	\(e\left(\frac{2}{9}\right)\)	\(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

(See \(a_n\) instead)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.17963	−	0.989828i	−0.834125	−	0.699914i	0.122109	−	0.992517i	\(-0.461034\pi\)
							−0.956234	+	0.292603i	\(0.905479\pi\)
\(3\)	0.853595	−	1.50711i	0.492824	−	0.870129i
							\(5\)	−1.99174	−	0.724932i	−0.890731	−	0.324200i	−0.144199	−	0.989549i	\(-0.546060\pi\)
−0.746532	+	0.665349i	\(0.768283\pi\)
\(7\)	0.173648	−	0.984808i	0.0656328	−	0.372222i
							\(11\)	−0.848433	+	0.308804i	−0.255812	+	0.0931081i	−0.466743	−	0.884393i	\(-0.654573\pi\)
0.210931	+	0.977501i	\(0.432351\pi\)
\(13\)	1.15251	−	0.967070i	0.319648	−	0.268217i	−0.468818	−	0.883295i	\(-0.655320\pi\)
							0.788466	+	0.615078i	\(0.210875\pi\)
\(17\)	0.841276	+	1.45713i	0.204039	+	0.353406i	0.949826	−	0.312778i	\(-0.101260\pi\)
							−0.745787	+	0.666185i	\(0.767926\pi\)
\(19\)	−1.00997	+	1.74932i	−0.231703	+	0.401322i	−0.958309	−	0.285732i	\(-0.907763\pi\)
							0.726606	+	0.687054i	\(0.241096\pi\)
\(23\)	−1.35659	−	7.69360i	−0.282868	−	1.60423i	−0.712801	−	0.701366i	\(-0.752574\pi\)
							0.429933	−	0.902861i	\(-0.358537\pi\)
\(29\)	0.185749	+	0.155862i	0.0344927	+	0.0289429i	0.659871	−	0.751379i	\(-0.270611\pi\)
							−0.625378	+	0.780322i	\(0.715055\pi\)
\(31\)	0.233808	+	1.32599i	0.0419932	+	0.238155i	0.998579	−	0.0532964i	\(-0.0169728\pi\)
							−0.956586	+	0.291452i	\(0.905862\pi\)
\(37\)	−1.42718	−	2.47195i	−0.234628	−	0.406387i	0.724537	−	0.689236i	\(-0.242054\pi\)
							−0.959164	+	0.282849i	\(0.908720\pi\)
\(41\)	7.73512	−	6.49053i	1.20802	−	1.01365i	0.208659	−	0.977989i	\(-0.433090\pi\)
							0.999364	−	0.0356626i	\(-0.0113542\pi\)
\(43\)	9.52529	−	3.46692i	1.45259	−	0.528701i	0.509279	−	0.860601i	\(-0.329912\pi\)
							0.943314	+	0.331900i	\(0.107690\pi\)
\(47\)	1.00540	−	5.70189i	0.146652	−	0.831707i	−0.819373	−	0.573260i	\(-0.805678\pi\)
							0.966026	−	0.258446i	\(-0.0832105\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.v.a.43.2	yes	54
3.2	odd	2		567.2.v.b.127.8		54
27.5	odd	18		567.2.v.b.442.8		54
27.7	even	9		5103.2.a.i.1.6		27
27.20	odd	18		5103.2.a.f.1.22		27
27.22	even	9	inner	189.2.v.a.22.2	✓	54

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.v.a.22.2	✓	54	27.22	even	9	inner
189.2.v.a.43.2	yes	54	1.1	even	1	trivial
567.2.v.b.127.8		54	3.2	odd	2
567.2.v.b.442.8		54	27.5	odd	18
5103.2.a.f.1.22		27	27.20	odd	18
5103.2.a.i.1.6		27	27.7	even	9