Embedded newform 567.2.br.a.101.57

• Label: 567.2.br.a.101.57
• 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			101.57
Character	\(\chi\)	\(=\)	567.101
Dual form			567.2.br.a.320.57

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.58545 - 1.18032i) q^{2} +(1.70739 + 0.291212i) q^{3} +(0.546879 - 1.82670i) q^{4} +(-0.138577 - 2.37927i) q^{5} +(3.05071 - 1.55358i) q^{6} +(-1.74527 - 1.98847i) q^{7} +(0.0629990 + 0.173088i) q^{8} +(2.83039 + 0.994426i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1260 q - 9 q^{2} - 27 q^{3} - 9 q^{4} - 27 q^{5} - 18 q^{7} - 36 q^{8} - 9 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.58545	−	1.18032i	1.12108	−	0.834614i	0.133395	−	0.991063i	\(-0.457412\pi\)
							0.987686	+	0.156449i	\(0.0500046\pi\)
\(3\)	1.70739	+	0.291212i	0.985765	+	0.168131i
							\(5\)	−0.138577	−	2.37927i	−0.0619733	−	1.06404i	−0.875720	−	0.482820i	\(-0.839612\pi\)
0.813746	−	0.581220i	\(-0.197425\pi\)
\(7\)	−1.74527	−	1.98847i	−0.659651	−	0.751572i
							\(11\)	−1.05160	+	1.59888i	−0.317069	+	0.482081i	−0.958497	−	0.285103i	\(-0.907972\pi\)
0.641427	+	0.767184i	\(0.278343\pi\)
\(13\)	−2.23357	−	1.66283i	−0.619480	−	0.461186i	0.241101	−	0.970500i	\(-0.422492\pi\)
							−0.860581	+	0.509314i	\(0.829899\pi\)
\(17\)	−0.890778	−	5.05186i	−0.216045	−	1.22525i	−0.879083	−	0.476669i	\(-0.841844\pi\)
							0.663038	−	0.748586i	\(-0.269267\pi\)
\(19\)	4.82762	+	0.851240i	1.10753	+	0.195288i	0.697361	−	0.716720i	\(-0.254358\pi\)
							0.410172	+	0.912008i	\(0.365469\pi\)
\(23\)	1.64598	+	6.94495i	0.343211	+	1.44812i	0.821646	+	0.569998i	\(0.193056\pi\)
							−0.478435	+	0.878123i	\(0.658796\pi\)
\(29\)	−4.71179	−	2.03247i	−0.874958	−	0.377420i	−0.0892440	−	0.996010i	\(-0.528445\pi\)
							−0.785714	+	0.618590i	\(0.787704\pi\)
\(31\)	2.50435	+	10.5667i	0.449795	+	1.89783i	0.440243	+	0.897879i	\(0.354892\pi\)
							0.00955171	+	0.999954i	\(0.496960\pi\)
\(37\)	−7.85226	+	6.58883i	−1.29090	+	1.08320i	−0.299263	+	0.954171i	\(0.596741\pi\)
							−0.991641	+	0.129026i	\(0.958815\pi\)
\(41\)	5.66631	+	0.662296i	0.884929	+	0.103433i	0.546402	−	0.837523i	\(-0.315997\pi\)
							0.338527	+	0.940957i	\(0.390071\pi\)
\(43\)	−8.81844	−	5.79998i	−1.34480	−	0.884489i	−0.346241	−	0.938146i	\(-0.612542\pi\)
							−0.998559	+	0.0536566i	\(0.982912\pi\)
\(47\)	7.11087	+	1.68531i	1.03723	+	0.245827i	0.713744	−	0.700407i	\(-0.246998\pi\)
							0.323483	+	0.946234i	\(0.395146\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.br.a.101.57	yes	1260
7.5	odd	6		567.2.bl.a.425.14	✓	1260
81.77	odd	54		567.2.bl.a.563.14	yes	1260
567.320	even	54	inner	567.2.br.a.320.57	yes	1260

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.bl.a.425.14	✓	1260	7.5	odd	6
567.2.bl.a.563.14	yes	1260	81.77	odd	54
567.2.br.a.101.57	yes	1260	1.1	even	1	trivial
567.2.br.a.320.57	yes	1260	567.320	even	54	inner