Embedded newform 567.2.br.a.101.42

• Label: 567.2.br.a.101.42
• 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			101.42
Character	\(\chi\)	\(=\)	567.101
Dual form			567.2.br.a.320.42

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.392975 - 0.292559i) q^{2} +(0.0592688 + 1.73104i) q^{3} +(-0.504768 + 1.68604i) q^{4} +(0.0409810 + 0.703616i) q^{5} +(0.529722 + 0.662915i) q^{6} +(1.61978 + 2.09196i) q^{7} +(0.630030 + 1.73099i) q^{8} +(-2.99297 + 0.205193i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1260 q - 9 q^{2} - 27 q^{3} - 9 q^{4} - 27 q^{5} - 18 q^{7} - 36 q^{8} - 9 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.392975	−	0.292559i	0.277875	−	0.206871i	−0.449194	−	0.893434i	\(-0.648289\pi\)
							0.727070	+	0.686563i	\(0.240882\pi\)
\(3\)	0.0592688	+	1.73104i	0.0342189	+	0.999414i
							\(5\)	0.0409810	+	0.703616i	0.0183272	+	0.314667i	0.994996	+	0.0999151i	\(0.0318571\pi\)
−0.976669	+	0.214751i	\(0.931106\pi\)
\(7\)	1.61978	+	2.09196i	0.612220	+	0.790688i
							\(11\)	−0.0658671	+	0.100146i	−0.0198597	+	0.0301952i	−0.845281	−	0.534322i	\(-0.820567\pi\)
0.825422	+	0.564517i	\(0.190937\pi\)
\(13\)	−0.278331	−	0.207210i	−0.0771952	−	0.0574697i	0.557869	−	0.829929i	\(-0.311619\pi\)
							−0.635064	+	0.772459i	\(0.719026\pi\)
\(17\)	−0.273629	−	1.55183i	−0.0663647	−	0.376373i	−0.999843	−	0.0177382i	\(-0.994353\pi\)
							0.933478	−	0.358635i	\(-0.116758\pi\)
\(19\)	0.821294	+	0.144816i	0.188418	+	0.0332231i	0.267061	−	0.963680i	\(-0.413948\pi\)
							−0.0786430	+	0.996903i	\(0.525059\pi\)
\(23\)	−1.37774	−	5.81314i	−0.287279	−	1.21212i	−0.904892	−	0.425642i	\(-0.860048\pi\)
							0.617613	−	0.786482i	\(-0.288100\pi\)
\(29\)	1.99483	+	0.860484i	0.370430	+	0.159788i	0.573153	−	0.819448i	\(-0.305720\pi\)
							−0.202723	+	0.979236i	\(0.564979\pi\)
\(31\)	1.41905	+	5.98743i	0.254868	+	1.07537i	0.938427	+	0.345478i	\(0.112283\pi\)
							−0.683558	+	0.729896i	\(0.739569\pi\)
\(37\)	−6.49377	+	5.44892i	−1.06757	+	0.895797i	−0.994830	−	0.101554i	\(-0.967618\pi\)
							−0.0727390	+	0.997351i	\(0.523174\pi\)
\(41\)	0.145836	+	0.0170458i	0.0227757	+	0.00266210i	0.127473	−	0.991842i	\(-0.459313\pi\)
							−0.104697	+	0.994504i	\(0.533387\pi\)
\(43\)	2.18211	+	1.43520i	0.332769	+	0.218866i	0.704887	−	0.709320i	\(-0.250998\pi\)
							−0.372118	+	0.928186i	\(0.621368\pi\)
\(47\)	4.35363	+	1.03183i	0.635042	+	0.150508i	0.535513	−	0.844527i	\(-0.320118\pi\)
							0.0995288	+	0.995035i	\(0.468266\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.br.a.101.42	yes	1260
7.5	odd	6		567.2.bl.a.425.29	✓	1260
81.77	odd	54		567.2.bl.a.563.29	yes	1260
567.320	even	54	inner	567.2.br.a.320.42	yes	1260

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.bl.a.425.29	✓	1260	7.5	odd	6
567.2.bl.a.563.29	yes	1260	81.77	odd	54
567.2.br.a.101.42	yes	1260	1.1	even	1	trivial
567.2.br.a.320.42	yes	1260	567.320	even	54	inner