Embedded newform 547.2.m.a.10.20

• Label: 547.2.m.a.10.20
• 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			10.20
Character	\(\chi\)	\(=\)	547.10
Dual form			547.2.m.a.383.20

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.290706 - 0.490397i) q^{2} +(0.429128 + 1.88013i) q^{3} +(0.803896 - 1.46948i) q^{4} +(-2.18526 - 0.0754717i) q^{5} +(0.797261 - 0.757008i) q^{6} +(-1.33797 + 0.185946i) q^{7} +(-2.09382 + 0.0723137i) q^{8} +(-0.647842 + 0.311984i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.290706	−	0.490397i	−0.205560	−	0.346763i	0.739780	−	0.672849i	\(-0.234929\pi\)
							−0.945340	+	0.326086i	\(0.894270\pi\)
\(3\)	0.429128	+	1.88013i	0.247757	+	1.08550i	0.933761	+	0.357897i	\(0.116506\pi\)
							−0.686004	+	0.727598i	\(0.740637\pi\)
\(5\)	−2.18526	−	0.0754717i	−0.977278	−	0.0337520i	−0.458530	−	0.888679i	\(-0.651624\pi\)
							−0.518748	+	0.854927i	\(0.673602\pi\)
\(7\)	−1.33797	+	0.185946i	−0.505705	+	0.0702811i	−0.385945	−	0.922522i	\(-0.626125\pi\)
							−0.119760	+	0.992803i	\(0.538212\pi\)
\(11\)	−0.631640	−	0.155685i	−0.190447	−	0.0469409i	0.142939	−	0.989732i	\(-0.454345\pi\)
							−0.333385	+	0.942791i	\(0.608191\pi\)
\(13\)	−4.22905	−	5.30306i	−1.17293	−	1.47080i	−0.851878	−	0.523740i	\(-0.824536\pi\)
							−0.321049	−	0.947063i	\(-0.604035\pi\)
\(17\)	6.11072	−	5.04812i	1.48207	−	1.22435i	0.565326	−	0.824867i	\(-0.308750\pi\)
							0.916741	−	0.399483i	\(-0.130810\pi\)
\(19\)	2.09626	−	1.29207i	0.480916	−	0.296421i	−0.262879	−	0.964829i	\(-0.584672\pi\)
							0.743795	+	0.668407i	\(0.233024\pi\)
\(23\)	1.03815	−	3.43565i	0.216469	−	0.716383i	−0.779477	−	0.626430i	\(-0.784515\pi\)
							0.995946	−	0.0899524i	\(-0.0286715\pi\)
\(29\)	−2.46329	+	1.40335i	−0.457422	+	0.260595i	−0.706263	−	0.707949i	\(-0.749620\pi\)
							0.248842	+	0.968544i	\(0.419950\pi\)
\(31\)	−7.71074	+	2.77303i	−1.38489	+	0.498051i	−0.921595	−	0.388153i	\(-0.873113\pi\)
							−0.463295	+	0.886204i	\(0.653333\pi\)
\(37\)	0.917406	−	5.85770i	0.150821	−	0.962999i	−0.787270	−	0.616609i	\(-0.788506\pi\)
							0.938090	−	0.346391i	\(-0.112593\pi\)
\(41\)	2.55578			0.399146			0.199573	−	0.979883i	\(-0.436044\pi\)
							0.199573	+	0.979883i	\(0.436044\pi\)
\(43\)	6.85516	−	4.90861i	1.04540	−	0.748556i	0.0767684	−	0.997049i	\(-0.475540\pi\)
							0.968634	+	0.248493i	\(0.0799354\pi\)
\(47\)	−3.04901	+	4.41725i	−0.444744	+	0.644323i	−0.979679	−	0.200570i	\(-0.935720\pi\)
							0.534936	+	0.844893i	\(0.320336\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.m.a.10.20	✓	3168
547.383	even	91	inner	547.2.m.a.383.20	yes	3168

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.m.a.10.20	✓	3168	1.1	even	1	trivial
547.2.m.a.383.20	yes	3168	547.383	even	91	inner