Embedded newform 567.2.br.a.101.12

• Label: 567.2.br.a.101.12
• 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			101.12
Character	\(\chi\)	\(=\)	567.101
Dual form			567.2.br.a.320.12

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.65607 + 1.23290i) q^{2} +(-0.571714 + 1.63498i) q^{3} +(0.648925 - 2.16756i) q^{4} +(-0.0690617 - 1.18574i) q^{5} +(-1.06896 - 3.41250i) q^{6} +(-1.59472 + 2.11113i) q^{7} +(0.185441 + 0.509495i) q^{8} +(-2.34629 - 1.86948i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1260 q - 9 q^{2} - 27 q^{3} - 9 q^{4} - 27 q^{5} - 18 q^{7} - 36 q^{8} - 9 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.65607	+	1.23290i	−1.17102	+	0.871792i	−0.993668	−	0.112356i	\(-0.964160\pi\)
							−0.177351	+	0.984148i	\(0.556753\pi\)
\(3\)	−0.571714	+	1.63498i	−0.330079	+	0.943953i
							\(5\)	−0.0690617	−	1.18574i	−0.0308853	−	0.530281i	−0.977898	−	0.209084i	\(-0.932952\pi\)
0.947012	−	0.321197i	\(-0.104085\pi\)
\(7\)	−1.59472	+	2.11113i	−0.602748	+	0.797932i
							\(11\)	−2.44289	+	3.71424i	−0.736560	+	1.11989i	0.251804	+	0.967778i	\(0.418976\pi\)
−0.988364	+	0.152107i	\(0.951394\pi\)
\(13\)	0.158117	+	0.117714i	0.0438539	+	0.0326480i	0.618862	−	0.785499i	\(-0.287594\pi\)
							−0.575008	+	0.818147i	\(0.695001\pi\)
\(17\)	−0.541162	−	3.06908i	−0.131251	−	0.744361i	−0.977397	−	0.211411i	\(-0.932194\pi\)
							0.846146	−	0.532951i	\(-0.178917\pi\)
\(19\)	−2.54099	−	0.448045i	−0.582943	−	0.102789i	−0.125603	−	0.992081i	\(-0.540087\pi\)
							−0.457340	+	0.889292i	\(0.651198\pi\)
\(23\)	−2.00227	−	8.44822i	−0.417501	−	1.76158i	−0.622307	−	0.782773i	\(-0.713804\pi\)
							0.204806	−	0.978803i	\(-0.434344\pi\)
\(29\)	−1.41854	−	0.611899i	−0.263416	−	0.113627i	0.260276	−	0.965534i	\(-0.416187\pi\)
							−0.523692	+	0.851908i	\(0.675446\pi\)
\(31\)	0.462033	+	1.94947i	0.0829836	+	0.350135i	0.998658	−	0.0517850i	\(-0.0164911\pi\)
							−0.915675	+	0.401920i	\(0.868343\pi\)
\(37\)	3.03699	−	2.54834i	0.499279	−	0.418945i	−0.358059	−	0.933699i	\(-0.616561\pi\)
							0.857338	+	0.514754i	\(0.172117\pi\)
\(41\)	1.70095	+	0.198813i	0.265644	+	0.0310494i	0.247872	−	0.968793i	\(-0.420269\pi\)
							0.0177719	+	0.999842i	\(0.494343\pi\)
\(43\)	4.13709	+	2.72100i	0.630900	+	0.414949i	0.824286	−	0.566173i	\(-0.191577\pi\)
							−0.193386	+	0.981123i	\(0.561947\pi\)
\(47\)	−5.32013	−	1.26089i	−0.776021	−	0.183920i	−0.176523	−	0.984297i	\(-0.556485\pi\)
							−0.599498	+	0.800376i	\(0.704633\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.br.a.101.12	yes	1260
7.5	odd	6		567.2.bl.a.425.59	✓	1260
81.77	odd	54		567.2.bl.a.563.59	yes	1260
567.320	even	54	inner	567.2.br.a.320.12	yes	1260

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.bl.a.425.59	✓	1260	7.5	odd	6
567.2.bl.a.563.59	yes	1260	81.77	odd	54
567.2.br.a.101.12	yes	1260	1.1	even	1	trivial
567.2.br.a.320.12	yes	1260	567.320	even	54	inner