Embedded newform 189.2.v.a.43.3

• Label: 189.2.v.a.43.3
• 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			43.3
Character	\(\chi\)	\(=\)	189.43
Dual form			189.2.v.a.22.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.09798 - 0.921318i) q^{2} +(-1.39977 + 1.02012i) q^{3} +(0.00944557 + 0.0535685i) q^{4} +(1.35272 + 0.492351i) q^{5} +(2.47678 + 0.169559i) q^{6} +(0.173648 - 0.984808i) q^{7} +(-1.39433 + 2.41506i) q^{8} +(0.918713 - 2.85587i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.09798	−	0.921318i	−0.776392	−	0.651470i	0.165945	−	0.986135i	\(-0.446932\pi\)
							−0.942337	+	0.334665i	\(0.891377\pi\)
\(3\)	−1.39977	+	1.02012i	−0.808158	+	0.588966i
							\(5\)	1.35272	+	0.492351i	0.604956	+	0.220186i	0.626295	−	0.779586i	\(-0.284571\pi\)
−0.0213385	+	0.999772i	\(0.506793\pi\)
\(7\)	0.173648	−	0.984808i	0.0656328	−	0.372222i
							\(11\)	1.39413	−	0.507422i	0.420346	−	0.152993i	−0.123183	−	0.992384i	\(-0.539310\pi\)
0.543529	+	0.839391i	\(0.317088\pi\)
\(13\)	3.79855	−	3.18736i	1.05353	−	0.884015i	0.0600674	−	0.998194i	\(-0.480868\pi\)
							0.993460	+	0.114180i	\(0.0364240\pi\)
\(17\)	−3.76596	−	6.52284i	−0.913380	−	1.58202i	−0.809256	−	0.587457i	\(-0.800129\pi\)
							−0.104125	−	0.994564i	\(-0.533204\pi\)
\(19\)	4.13067	−	7.15453i	0.947641	−	1.64136i	0.197265	−	0.980350i	\(-0.436794\pi\)
							0.750376	−	0.661012i	\(-0.229873\pi\)
\(23\)	1.31455	+	7.45520i	0.274103	+	1.55452i	0.741796	+	0.670625i	\(0.233974\pi\)
							−0.467693	+	0.883891i	\(0.654915\pi\)
\(29\)	0.675850	+	0.567105i	0.125502	+	0.105309i	0.703378	−	0.710816i	\(-0.251674\pi\)
							−0.577876	+	0.816124i	\(0.696118\pi\)
\(31\)	1.22342	+	6.93837i	0.219733	+	1.24617i	0.872502	+	0.488611i	\(0.162496\pi\)
							−0.652769	+	0.757557i	\(0.726393\pi\)
\(37\)	0.822178	+	1.42405i	0.135165	+	0.234113i	0.925661	−	0.378355i	\(-0.123510\pi\)
							−0.790495	+	0.612468i	\(0.790177\pi\)
\(41\)	7.19412	−	6.03659i	1.12353	−	0.942756i	0.124756	−	0.992187i	\(-0.460185\pi\)
							0.998778	+	0.0494312i	\(0.0157409\pi\)
\(43\)	−1.81964	+	0.662296i	−0.277493	+	0.100999i	−0.477018	−	0.878894i	\(-0.658282\pi\)
							0.199525	+	0.979893i	\(0.436060\pi\)
\(47\)	−0.0880328	+	0.499259i	−0.0128409	+	0.0728244i	−0.990555	−	0.137117i	\(-0.956216\pi\)
							0.977714	+	0.209942i	\(0.0673274\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.v.a.43.3	yes	54
3.2	odd	2		567.2.v.b.127.7		54
27.5	odd	18		567.2.v.b.442.7		54
27.7	even	9		5103.2.a.i.1.7		27
27.20	odd	18		5103.2.a.f.1.21		27
27.22	even	9	inner	189.2.v.a.22.3	✓	54

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.v.a.22.3	✓	54	27.22	even	9	inner
189.2.v.a.43.3	yes	54	1.1	even	1	trivial
567.2.v.b.127.7		54	3.2	odd	2
567.2.v.b.442.7		54	27.5	odd	18
5103.2.a.f.1.21		27	27.20	odd	18
5103.2.a.i.1.7		27	27.7	even	9