Embedded newform 273.2.br.b.17.5

• Label: 273.2.br.b.17.5
• Level: $273$
• Weight: $2$
• Character: 273.17
• Analytic conductor: $2.180$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.br (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.17991597518\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.5
Character	\(\chi\)	\(=\)	273.17
Dual form			273.2.br.b.257.5

$q$-expansion

\(f(q)\)	\(=\)	\(q-2.13558 q^{2} +(-1.59741 - 0.669547i) q^{3} +2.56071 q^{4} +(-3.07271 + 1.77403i) q^{5} +(3.41139 + 1.42987i) q^{6} +(-1.82045 + 1.91989i) q^{7} -1.19745 q^{8} +(2.10341 + 2.13908i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{3} + 56 q^{4} - 6 q^{7}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\)	\(92\)	\(106\)	\(157\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.13558			−1.51008			−0.755042	−	0.655676i	\(-0.772384\pi\)
							−0.755042	+	0.655676i	\(0.772384\pi\)
\(3\)	−1.59741	−	0.669547i	−0.922263	−	0.386563i
							\(5\)	−3.07271	+	1.77403i	−1.37416	+	0.793370i	−0.991448	−	0.130499i	\(-0.958342\pi\)
−0.382709	+	0.923869i	\(0.625009\pi\)
\(7\)	−1.82045	+	1.91989i	−0.688064	+	0.725650i
							\(11\)	0.843639	+	1.46123i	0.254367	+	0.440576i	0.964723	−	0.263266i	\(-0.0847997\pi\)
−0.710357	+	0.703842i	\(0.751466\pi\)
\(13\)	−0.905061	−	3.49011i	−0.251019	−	0.967982i
							\(17\)	−2.50797			−0.608273			−0.304136	−	0.952628i	\(-0.598368\pi\)
−0.304136	+	0.952628i	\(0.598368\pi\)
\(19\)	−1.66686	+	2.88709i	−0.382404	+	0.662343i	−0.991405	−	0.130826i	\(-0.958237\pi\)
							0.609001	+	0.793169i	\(0.291570\pi\)
\(23\)		−	7.63380i		−	1.59176i	−0.605457	−	0.795878i	\(-0.707009\pi\)
							0.605457	−	0.795878i	\(-0.292991\pi\)
\(29\)	3.85641	+	2.22650i	0.716117	+	0.413450i	0.813322	−	0.581814i	\(-0.197657\pi\)
							−0.0972050	+	0.995264i	\(0.530990\pi\)
\(31\)	5.26838	−	9.12510i	0.946229	−	1.63892i	0.192958	−	0.981207i	\(-0.438192\pi\)
							0.753271	−	0.657710i	\(-0.228475\pi\)
\(37\)			5.55358i			0.913002i	0.889723	+	0.456501i	\(0.150898\pi\)
							−0.889723	+	0.456501i	\(0.849102\pi\)
\(41\)	−2.89982	−	1.67421i	−0.452875	−	0.261468i	0.256169	−	0.966632i	\(-0.417540\pi\)
							−0.709044	+	0.705165i	\(0.750873\pi\)
\(43\)	−0.303610	−	0.525869i	−0.0463002	−	0.0801942i	0.841947	−	0.539561i	\(-0.181410\pi\)
							−0.888247	+	0.459367i	\(0.848076\pi\)
\(47\)	1.95815	−	1.13054i	0.285626	−	0.164906i	−0.350342	−	0.936622i	\(-0.613935\pi\)
							0.635968	+	0.771716i	\(0.280601\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.br.b.17.5	yes	64
3.2	odd	2	inner	273.2.br.b.17.28	yes	64
7.5	odd	6		273.2.y.b.173.28	yes	64
13.10	even	6		273.2.y.b.101.5	✓	64
21.5	even	6		273.2.y.b.173.5	yes	64
39.23	odd	6		273.2.y.b.101.28	yes	64
91.75	odd	6	inner	273.2.br.b.257.28	yes	64
273.257	even	6	inner	273.2.br.b.257.5	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.y.b.101.5	✓	64	13.10	even	6
273.2.y.b.101.28	yes	64	39.23	odd	6
273.2.y.b.173.5	yes	64	21.5	even	6
273.2.y.b.173.28	yes	64	7.5	odd	6
273.2.br.b.17.5	yes	64	1.1	even	1	trivial
273.2.br.b.17.28	yes	64	3.2	odd	2	inner
273.2.br.b.257.5	yes	64	273.257	even	6	inner
273.2.br.b.257.28	yes	64	91.75	odd	6	inner