Embedded newform 273.2.y.b.101.6

• Label: 273.2.y.b.101.6
• 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			101.6
Character	\(\chi\)	\(=\)	273.101
Dual form			273.2.y.b.173.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.985417 + 1.70679i) q^{2} +(-0.524054 + 1.65087i) q^{3} +(-0.942093 - 1.63175i) q^{4} +(-0.0906165 + 0.0523174i) q^{5} +(-2.30128 - 2.52124i) q^{6} +(0.412313 - 2.61343i) q^{7} -0.228249 q^{8} +(-2.45074 - 1.73029i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 28 q^{4} - 12 q^{7}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.985417	+	1.70679i	−0.696795	+	1.20688i	0.272777	+	0.962077i	\(0.412058\pi\)
							−0.969572	+	0.244807i	\(0.921275\pi\)
\(3\)	−0.524054	+	1.65087i	−0.302563	+	0.953130i
							\(5\)	−0.0906165	+	0.0523174i	−0.0405249	+	0.0233971i	−0.520126	−	0.854090i	\(-0.674115\pi\)
0.479601	+	0.877487i	\(0.340782\pi\)
\(7\)	0.412313	−	2.61343i	0.155840	−	0.987782i
							\(11\)	−5.74169			−1.73119			−0.865593	−	0.500749i	\(-0.833058\pi\)
−0.865593	+	0.500749i	\(0.833058\pi\)
\(13\)	−3.31340	+	1.42176i	−0.918971	+	0.394324i
							\(17\)	−0.965258	−	1.67188i	−0.234110	−	0.405490i	0.724904	−	0.688850i	\(-0.241884\pi\)
−0.959014	+	0.283360i	\(0.908551\pi\)
\(19\)	−0.278245			−0.0638339			−0.0319169	−	0.999491i	\(-0.510161\pi\)
							−0.0319169	+	0.999491i	\(0.510161\pi\)
\(23\)	6.41681	+	3.70475i	1.33800	+	0.772493i	0.986510	−	0.163700i	\(-0.0523428\pi\)
							0.351487	+	0.936193i	\(0.385676\pi\)
\(29\)	−3.16433	+	1.82693i	−0.587602	+	0.339252i	−0.764149	−	0.645040i	\(-0.776841\pi\)
							0.176547	+	0.984292i	\(0.443507\pi\)
\(31\)	−4.20000	+	7.27462i	−0.754343	+	1.30656i	0.191358	+	0.981520i	\(0.438711\pi\)
							−0.945700	+	0.325040i	\(0.894622\pi\)
\(37\)	−4.55928	−	2.63230i	−0.749542	−	0.432748i	0.0759866	−	0.997109i	\(-0.475789\pi\)
							−0.825528	+	0.564361i	\(0.809123\pi\)
\(41\)	3.69487	−	2.13323i	0.577041	−	0.333155i	−0.182916	−	0.983129i	\(-0.558553\pi\)
							0.759957	+	0.649974i	\(0.225220\pi\)
\(43\)	−2.47429	+	4.28560i	−0.377326	+	0.653547i	−0.990672	−	0.136267i	\(-0.956490\pi\)
							0.613346	+	0.789814i	\(0.289823\pi\)
\(47\)	5.62823	−	3.24946i	0.820962	−	0.473983i	−0.0297859	−	0.999556i	\(-0.509483\pi\)
							0.850748	+	0.525574i	\(0.176149\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.y.b.101.6	✓	64
3.2	odd	2	inner	273.2.y.b.101.27	yes	64
7.5	odd	6		273.2.br.b.257.27	yes	64
13.4	even	6		273.2.br.b.17.6	yes	64
21.5	even	6		273.2.br.b.257.6	yes	64
39.17	odd	6		273.2.br.b.17.27	yes	64
91.82	odd	6	inner	273.2.y.b.173.27	yes	64
273.173	even	6	inner	273.2.y.b.173.6	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.y.b.101.6	✓	64	1.1	even	1	trivial
273.2.y.b.101.27	yes	64	3.2	odd	2	inner
273.2.y.b.173.6	yes	64	273.173	even	6	inner
273.2.y.b.173.27	yes	64	91.82	odd	6	inner
273.2.br.b.17.6	yes	64	13.4	even	6
273.2.br.b.17.27	yes	64	39.17	odd	6
273.2.br.b.257.6	yes	64	21.5	even	6
273.2.br.b.257.27	yes	64	7.5	odd	6