Embedded newform 189.2.v.b.43.5

• Label: 189.2.v.b.43.5
• 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			43.5
Character	\(\chi\)	\(=\)	189.43
Dual form			189.2.v.b.22.5

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.246848 - 0.207130i) q^{2} +(-0.915107 - 1.47057i) q^{3} +(-0.329265 - 1.86736i) q^{4} +(-1.61217 - 0.586782i) q^{5} +(-0.0787071 + 0.552555i) q^{6} +(-0.173648 + 0.984808i) q^{7} +(-0.627745 + 1.08729i) q^{8} +(-1.32516 + 2.69146i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 3 q^{3} - 3 q^{5} + 9 q^{8} + 3 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.246848	−	0.207130i	−0.174548	−	0.146463i	0.551328	−	0.834288i	\(-0.314121\pi\)
							−0.725877	+	0.687825i	\(0.758566\pi\)
\(3\)	−0.915107	−	1.47057i	−0.528338	−	0.849034i
							\(5\)	−1.61217	−	0.586782i	−0.720985	−	0.262417i	−0.0446411	−	0.999003i	\(-0.514214\pi\)
−0.676344	+	0.736586i	\(0.736437\pi\)
\(7\)	−0.173648	+	0.984808i	−0.0656328	+	0.372222i
							\(11\)	−2.40606	+	0.875734i	−0.725455	+	0.264044i	−0.678240	−	0.734841i	\(-0.737257\pi\)
−0.0472150	+	0.998885i	\(0.515035\pi\)
\(13\)	0.907822	−	0.761753i	0.251785	−	0.211272i	−0.508156	−	0.861265i	\(-0.669673\pi\)
							0.759940	+	0.649993i	\(0.225228\pi\)
\(17\)	−2.01797	−	3.49523i	−0.489430	−	0.847717i	0.510496	−	0.859880i	\(-0.329462\pi\)
							−0.999926	+	0.0121626i	\(0.996128\pi\)
\(19\)	3.61402	−	6.25967i	0.829114	−	1.43607i	−0.0696207	−	0.997574i	\(-0.522179\pi\)
							0.898734	−	0.438493i	\(-0.144488\pi\)
\(23\)	0.0639018	+	0.362405i	0.0133244	+	0.0755667i	0.990745	−	0.135737i	\(-0.0433402\pi\)
							−0.977420	+	0.211304i	\(0.932229\pi\)
\(29\)	−2.90659	−	2.43892i	−0.539741	−	0.452897i	0.331708	−	0.943382i	\(-0.392375\pi\)
							−0.871449	+	0.490485i	\(0.836819\pi\)
\(31\)	−1.27867	−	7.25168i	−0.229655	−	1.30244i	−0.853582	−	0.520958i	\(-0.825575\pi\)
							0.623927	−	0.781483i	\(-0.285536\pi\)
\(37\)	2.79726	+	4.84499i	0.459866	+	0.796512i	0.998953	−	0.0457383i	\(-0.0145640\pi\)
							−0.539087	+	0.842250i	\(0.681231\pi\)
\(41\)	−7.63600	+	6.40736i	−1.19254	+	1.00066i	−0.192730	+	0.981252i	\(0.561734\pi\)
							−0.999812	+	0.0194099i	\(0.993821\pi\)
\(43\)	2.38561	−	0.868290i	0.363802	−	0.132413i	−0.153650	−	0.988125i	\(-0.549103\pi\)
							0.517452	+	0.855712i	\(0.326881\pi\)
\(47\)	1.60222	−	9.08663i	0.233708	−	1.32542i	−0.611611	−	0.791159i	\(-0.709478\pi\)
							0.845318	−	0.534263i	\(-0.179411\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.v.b.43.5	yes	54
3.2	odd	2		567.2.v.a.127.5		54
27.5	odd	18		567.2.v.a.442.5		54
27.7	even	9		5103.2.a.g.1.13		27
27.20	odd	18		5103.2.a.h.1.15		27
27.22	even	9	inner	189.2.v.b.22.5	✓	54

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.v.b.22.5	✓	54	27.22	even	9	inner
189.2.v.b.43.5	yes	54	1.1	even	1	trivial
567.2.v.a.127.5		54	3.2	odd	2
567.2.v.a.442.5		54	27.5	odd	18
5103.2.a.g.1.13		27	27.7	even	9
5103.2.a.h.1.15		27	27.20	odd	18