Embedded newform 547.2.m.a.10.17

• Label: 547.2.m.a.10.17
• Level: $547$
• Weight: $2$
• Character: 547.10
• Analytic conductor: $4.368$
• Analytic rank: $0$
• Dimension: $3168$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.m (of order \(91\), degree \(72\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.36781699056\)
Analytic rank:	\(0\)
Dimension:	\(3168\)
Relative dimension:	\(44\) over \(\Q(\zeta_{91})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{91}]$

Embedding invariants

Embedding label			10.17
Character	\(\chi\)	\(=\)	547.10
Dual form			547.2.m.a.383.17

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.449712 - 0.758628i) q^{2} +(-0.258554 - 1.13280i) q^{3} +(0.586600 - 1.07228i) q^{4} +(0.442256 + 0.0152741i) q^{5} +(-0.743097 + 0.705579i) q^{6} +(-1.14748 + 0.159473i) q^{7} +(-2.84002 + 0.0980850i) q^{8} +(1.48653 - 0.715873i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/547\mathbb{Z}\right)^\times\).

\(n\)	\(2\)
\(\chi(n)\)	\(e\left(\frac{30}{91}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.449712	−	0.758628i	−0.317995	−	0.536431i	0.658333	−	0.752727i	\(-0.271262\pi\)
							−0.976328	+	0.216296i	\(0.930602\pi\)
\(3\)	−0.258554	−	1.13280i	−0.149276	−	0.654021i	−0.993087	−	0.117380i	\(-0.962550\pi\)
							0.843811	−	0.536640i	\(-0.180307\pi\)
\(5\)	0.442256	+	0.0152741i	0.197783	+	0.00683078i	0.133238	−	0.991084i	\(-0.457462\pi\)
							0.0645448	+	0.997915i	\(0.479440\pi\)
\(7\)	−1.14748	+	0.159473i	−0.433708	+	0.0602752i	−0.351168	−	0.936312i	\(-0.614215\pi\)
							−0.0825402	+	0.996588i	\(0.526303\pi\)
\(11\)	−5.77387	−	1.42313i	−1.74089	−	0.429090i	−0.764413	−	0.644727i	\(-0.776971\pi\)
							−0.976474	+	0.215636i	\(0.930817\pi\)
\(13\)	0.702602	+	0.881034i	0.194867	+	0.244355i	0.869659	−	0.493652i	\(-0.164338\pi\)
							−0.674793	+	0.738007i	\(0.735767\pi\)
\(17\)	2.74398	−	2.26683i	0.665513	−	0.549787i	−0.241756	−	0.970337i	\(-0.577723\pi\)
							0.907269	+	0.420550i	\(0.138163\pi\)
\(19\)	−7.08505	+	4.36700i	−1.62542	+	1.00186i	−0.656555	+	0.754278i	\(0.727987\pi\)
							−0.968867	+	0.247580i	\(0.920365\pi\)
\(23\)	1.96205	−	6.49321i	0.409115	−	1.35393i	−0.472239	−	0.881471i	\(-0.656554\pi\)
							0.881354	−	0.472457i	\(-0.156633\pi\)
\(29\)	4.72155	−	2.68988i	0.876770	−	0.499499i	0.0109988	−	0.999940i	\(-0.496499\pi\)
							0.865771	+	0.500440i	\(0.166829\pi\)
\(31\)	6.05332	−	2.17697i	1.08721	−	0.390995i	0.267372	−	0.963593i	\(-0.413845\pi\)
							0.819836	+	0.572599i	\(0.194065\pi\)
\(37\)	−0.638843	+	4.07905i	−0.105025	+	0.670592i	0.876807	+	0.480842i	\(0.159669\pi\)
							−0.981832	+	0.189750i	\(0.939232\pi\)
\(41\)	5.07130			0.792005			0.396002	−	0.918250i	\(-0.370397\pi\)
							0.396002	+	0.918250i	\(0.370397\pi\)
\(43\)	−4.75811	+	3.40703i	−0.725606	+	0.519567i	−0.883814	−	0.467839i	\(-0.845033\pi\)
							0.158208	+	0.987406i	\(0.449428\pi\)
\(47\)	0.621755	−	0.900767i	0.0906922	−	0.131390i	−0.775011	−	0.631947i	\(-0.782256\pi\)
							0.865704	+	0.500557i	\(0.166871\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.m.a.10.17	✓	3168
547.383	even	91	inner	547.2.m.a.383.17	yes	3168

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.m.a.10.17	✓	3168	1.1	even	1	trivial
547.2.m.a.383.17	yes	3168	547.383	even	91	inner