Embedded newform 567.2.br.a.101.45

• Label: 567.2.br.a.101.45
• 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			101.45
Character	\(\chi\)	\(=\)	567.101
Dual form			567.2.br.a.320.45

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.756088 - 0.562887i) q^{2} +(0.968358 + 1.43606i) q^{3} +(-0.318779 + 1.06479i) q^{4} +(0.203475 + 3.49353i) q^{5} +(1.54051 + 0.540716i) q^{6} +(-2.37705 - 1.16174i) q^{7} +(1.00312 + 2.75604i) q^{8} +(-1.12456 + 2.78125i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1260 q - 9 q^{2} - 27 q^{3} - 9 q^{4} - 27 q^{5} - 18 q^{7} - 36 q^{8} - 9 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.756088	−	0.562887i	0.534635	−	0.398021i	−0.295704	−	0.955280i	\(-0.595554\pi\)
							0.830339	+	0.557259i	\(0.188147\pi\)
\(3\)	0.968358	+	1.43606i	0.559082	+	0.829112i
							\(5\)	0.203475	+	3.49353i	0.0909967	+	1.56235i	0.667095	+	0.744972i	\(0.267537\pi\)
−0.576099	+	0.817380i	\(0.695426\pi\)
\(7\)	−2.37705	−	1.16174i	−0.898441	−	0.439095i
							\(11\)	2.45444	−	3.73179i	0.740041	−	1.12518i	−0.247664	−	0.968846i	\(-0.579663\pi\)
0.987705	−	0.156331i	\(-0.0499667\pi\)
\(13\)	−1.87976	−	1.39943i	−0.521350	−	0.388131i	0.304070	−	0.952650i	\(-0.401654\pi\)
							−0.825420	+	0.564519i	\(0.809062\pi\)
\(17\)	−0.694150	−	3.93672i	−0.168356	−	0.954795i	−0.945536	−	0.325517i	\(-0.894462\pi\)
							0.777180	−	0.629278i	\(-0.216649\pi\)
\(19\)	0.775361	+	0.136717i	0.177880	+	0.0313651i	0.261879	−	0.965101i	\(-0.415658\pi\)
							−0.0839985	+	0.996466i	\(0.526769\pi\)
\(23\)	1.04274	+	4.39965i	0.217426	+	0.917390i	0.966859	+	0.255311i	\(0.0821778\pi\)
							−0.749434	+	0.662080i	\(0.769674\pi\)
\(29\)	8.91155	+	3.84407i	1.65483	+	0.713825i	0.999150	−	0.0412121i	\(-0.0131219\pi\)
							0.655682	+	0.755037i	\(0.272381\pi\)
\(31\)	1.82048	+	7.68123i	0.326969	+	1.37959i	0.849779	+	0.527140i	\(0.176736\pi\)
							−0.522810	+	0.852449i	\(0.675116\pi\)
\(37\)	4.71084	−	3.95286i	0.774457	−	0.649847i	−0.167389	−	0.985891i	\(-0.553534\pi\)
							0.941846	+	0.336044i	\(0.109089\pi\)
\(41\)	−0.785105	−	0.0917656i	−0.122613	−	0.0143314i	0.0545652	−	0.998510i	\(-0.482623\pi\)
							−0.177178	+	0.984179i	\(0.556697\pi\)
\(43\)	7.78577	+	5.12078i	1.18732	+	0.780912i	0.980317	−	0.197428i	\(-0.0632589\pi\)
							0.207002	+	0.978340i	\(0.433629\pi\)
\(47\)	−8.34068	−	1.97678i	−1.21661	−	0.288343i	−0.428312	−	0.903631i	\(-0.640891\pi\)
							−0.788302	+	0.615288i	\(0.789040\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.br.a.101.45	yes	1260
7.5	odd	6		567.2.bl.a.425.26	✓	1260
81.77	odd	54		567.2.bl.a.563.26	yes	1260
567.320	even	54	inner	567.2.br.a.320.45	yes	1260

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.bl.a.425.26	✓	1260	7.5	odd	6
567.2.bl.a.563.26	yes	1260	81.77	odd	54
567.2.br.a.101.45	yes	1260	1.1	even	1	trivial
567.2.br.a.320.45	yes	1260	567.320	even	54	inner