Embedded newform 567.2.br.a.101.54

• Label: 567.2.br.a.101.54
• Level: $567$
• Weight: $2$
• Character: 567.101
• Analytic conductor: $4.528$
• Analytic rank: $0$
• Dimension: $1260$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.br (of order \(54\), degree \(18\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.52751779461\)
Analytic rank:	\(0\)
Dimension:	\(1260\)
Relative dimension:	\(70\) over \(\Q(\zeta_{54})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			101.54
Character	\(\chi\)	\(=\)	567.101
Dual form			567.2.br.a.320.54

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.35424 - 1.00819i) q^{2} +(-1.13601 + 1.30747i) q^{3} +(0.243903 - 0.814692i) q^{4} +(-0.0583696 - 1.00217i) q^{5} +(-0.220237 + 2.91595i) q^{6} +(2.63820 + 0.199764i) q^{7} +(0.663813 + 1.82381i) q^{8} +(-0.418979 - 2.97060i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1260 q - 9 q^{2} - 27 q^{3} - 9 q^{4} - 27 q^{5} - 18 q^{7} - 36 q^{8} - 9 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\)	\(325\)	\(407\)
\(\chi(n)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{54}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.35424	−	1.00819i	0.957592	−	0.712901i	−0.000309123	−	1.00000i	\(-0.500098\pi\)
							0.957901	+	0.287099i	\(0.0926910\pi\)
\(3\)	−1.13601	+	1.30747i	−0.655874	+	0.754871i
							\(5\)	−0.0583696	−	1.00217i	−0.0261037	−	0.448183i	−0.985884	−	0.167431i	\(-0.946453\pi\)
0.959780	−	0.280753i	\(-0.0905840\pi\)
\(7\)	2.63820	+	0.199764i	0.997146	+	0.0755037i
							\(11\)	−1.62803	+	2.47530i	−0.490869	+	0.746330i	−0.992956	−	0.118488i	\(-0.962195\pi\)
0.502087	+	0.864817i	\(0.332566\pi\)
\(13\)	3.12458	+	2.32616i	0.866602	+	0.645162i	0.935835	−	0.352439i	\(-0.114648\pi\)
							−0.0692324	+	0.997601i	\(0.522055\pi\)
\(17\)	−0.637596	−	3.61598i	−0.154640	−	0.877005i	−0.959114	−	0.283018i	\(-0.908664\pi\)
							0.804475	−	0.593987i	\(-0.202447\pi\)
\(19\)	−1.40292	−	0.247372i	−0.321851	−	0.0567511i	0.0103885	−	0.999946i	\(-0.496693\pi\)
							−0.332240	+	0.943195i	\(0.607804\pi\)
\(23\)	1.77376	+	7.48410i	0.369856	+	1.56054i	0.766299	+	0.642484i	\(0.222096\pi\)
							−0.396444	+	0.918059i	\(0.629756\pi\)
\(29\)	6.00709	+	2.59121i	1.11549	+	0.481175i	0.872382	−	0.488825i	\(-0.162574\pi\)
							0.243107	+	0.970000i	\(0.421834\pi\)
\(31\)	−0.0364536	−	0.153810i	−0.00654725	−	0.0276250i	0.969673	−	0.244405i	\(-0.0785927\pi\)
							−0.976220	+	0.216780i	\(0.930445\pi\)
\(37\)	9.07090	−	7.61139i	1.49125	−	1.25131i	0.598196	−	0.801350i	\(-0.295884\pi\)
							0.893051	−	0.449956i	\(-0.148560\pi\)
\(41\)	−7.93164	−	0.927076i	−1.23871	−	0.144785i	−0.528600	−	0.848871i	\(-0.677283\pi\)
							−0.710114	+	0.704086i	\(0.751357\pi\)
\(43\)	−9.37588	−	6.16661i	−1.42981	−	0.940399i	−0.999285	−	0.0378199i	\(-0.987959\pi\)
							−0.430523	−	0.902579i	\(-0.641671\pi\)
\(47\)	−9.12952	−	2.16374i	−1.33168	−	0.315613i	−0.497670	−	0.867367i	\(-0.665811\pi\)
							−0.834007	+	0.551753i	\(0.813959\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.br.a.101.54	yes	1260
7.5	odd	6		567.2.bl.a.425.17	✓	1260
81.77	odd	54		567.2.bl.a.563.17	yes	1260
567.320	even	54	inner	567.2.br.a.320.54	yes	1260

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.bl.a.425.17	✓	1260	7.5	odd	6
567.2.bl.a.563.17	yes	1260	81.77	odd	54
567.2.br.a.101.54	yes	1260	1.1	even	1	trivial
567.2.br.a.320.54	yes	1260	567.320	even	54	inner