Embedded newform 273.2.y.b.101.14

• Label: 273.2.y.b.101.14
• Level: $273$
• Weight: $2$
• Character: 273.101
• 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.y (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			101.14
Character	\(\chi\)	\(=\)	273.101
Dual form			273.2.y.b.173.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.209784 + 0.363356i) q^{2} +(0.760555 - 1.55614i) q^{3} +(0.911982 + 1.57960i) q^{4} +(3.21070 - 1.85370i) q^{5} +(0.405879 + 0.602804i) q^{6} +(2.20704 + 1.45910i) q^{7} -1.60441 q^{8} +(-1.84311 - 2.36705i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 28 q^{4} - 12 q^{7}+O(q^{10}) \)

Character values

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

\(n\)	\(92\)	\(106\)	\(157\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.209784	+	0.363356i	−0.148339	+	0.256931i	−0.930614	−	0.366003i	\(-0.880726\pi\)
							0.782274	+	0.622934i	\(0.214059\pi\)
\(3\)	0.760555	−	1.55614i	0.439106	−	0.898435i
							\(5\)	3.21070	−	1.85370i	1.43587	−	0.828998i	0.438308	−	0.898825i	\(-0.355578\pi\)
0.997559	+	0.0698271i	\(0.0222447\pi\)
\(7\)	2.20704	+	1.45910i	0.834184	+	0.551487i
							\(11\)	−4.50522			−1.35838			−0.679188	−	0.733964i	\(-0.737668\pi\)
−0.679188	+	0.733964i	\(0.737668\pi\)
\(13\)	−2.65882	+	2.43530i	−0.737423	+	0.675431i
							\(17\)	−0.934314	−	1.61828i	−0.226604	−	0.392490i	0.730195	−	0.683239i	\(-0.239429\pi\)
−0.956800	+	0.290748i	\(0.906096\pi\)
\(19\)	2.02889			0.465460			0.232730	−	0.972541i	\(-0.425234\pi\)
							0.232730	+	0.972541i	\(0.425234\pi\)
\(23\)	1.48420	+	0.856903i	0.309477	+	0.178677i	0.646693	−	0.762751i	\(-0.276152\pi\)
							−0.337215	+	0.941428i	\(0.609485\pi\)
\(29\)	−0.535895	+	0.309399i	−0.0995133	+	0.0574540i	−0.548931	−	0.835868i	\(-0.684965\pi\)
							0.449417	+	0.893322i	\(0.351632\pi\)
\(31\)	0.476920	−	0.826049i	0.0856573	−	0.148363i	−0.820014	−	0.572344i	\(-0.806034\pi\)
							0.905671	+	0.423981i	\(0.139368\pi\)
\(37\)	−5.10600	−	2.94795i	−0.839421	−	0.484640i	0.0176462	−	0.999844i	\(-0.494383\pi\)
							−0.857067	+	0.515204i	\(0.827716\pi\)
\(41\)	5.98390	−	3.45481i	0.934528	−	0.539550i	0.0462874	−	0.998928i	\(-0.485261\pi\)
							0.888241	+	0.459378i	\(0.151928\pi\)
\(43\)	−1.32592	+	2.29655i	−0.202200	+	0.350221i	−0.949237	−	0.314562i	\(-0.898142\pi\)
							0.747037	+	0.664783i	\(0.231476\pi\)
\(47\)	−10.1715	+	5.87250i	−1.48366	+	0.856593i	−0.999828	−	0.0185665i	\(-0.994090\pi\)
							−0.483835	+	0.875159i	\(0.660756\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.y.b.101.14	✓	64
3.2	odd	2	inner	273.2.y.b.101.19	yes	64
7.5	odd	6		273.2.br.b.257.19	yes	64
13.4	even	6		273.2.br.b.17.14	yes	64
21.5	even	6		273.2.br.b.257.14	yes	64
39.17	odd	6		273.2.br.b.17.19	yes	64
91.82	odd	6	inner	273.2.y.b.173.19	yes	64
273.173	even	6	inner	273.2.y.b.173.14	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.y.b.101.14	✓	64	1.1	even	1	trivial
273.2.y.b.101.19	yes	64	3.2	odd	2	inner
273.2.y.b.173.14	yes	64	273.173	even	6	inner
273.2.y.b.173.19	yes	64	91.82	odd	6	inner
273.2.br.b.17.14	yes	64	13.4	even	6
273.2.br.b.17.19	yes	64	39.17	odd	6
273.2.br.b.257.14	yes	64	21.5	even	6
273.2.br.b.257.19	yes	64	7.5	odd	6