Embedded newform 273.2.y.b.101.11

• Label: 273.2.y.b.101.11
• 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			101.11
Character	\(\chi\)	\(=\)	273.101
Dual form			273.2.y.b.173.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.636825 + 1.10301i) q^{2} +(0.696603 + 1.58579i) q^{3} +(0.188907 + 0.327197i) q^{4} +(1.93046 - 1.11455i) q^{5} +(-2.19277 - 0.241511i) q^{6} +(-2.30379 + 1.30098i) q^{7} -3.02850 q^{8} +(-2.02949 + 2.20934i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 28 q^{4} - 12 q^{7}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.636825	+	1.10301i	−0.450303	+	0.779949i	−0.998405	−	0.0564635i	\(-0.982018\pi\)
							0.548101	+	0.836412i	\(0.315351\pi\)
\(3\)	0.696603	+	1.58579i	0.402184	+	0.915559i
							\(5\)	1.93046	−	1.11455i	0.863326	−	0.498441i	−0.00179877	−	0.999998i	\(-0.500573\pi\)
0.865125	+	0.501557i	\(0.167239\pi\)
\(7\)	−2.30379	+	1.30098i	−0.870751	+	0.491725i
							\(11\)	3.98376			1.20115			0.600575	−	0.799569i	\(-0.294938\pi\)
0.600575	+	0.799569i	\(0.294938\pi\)
\(13\)	−0.567682	+	3.56058i	−0.157447	+	0.987528i
							\(17\)	−2.24287	−	3.88476i	−0.543976	−	0.942194i	−0.998671	−	0.0515463i	\(-0.983585\pi\)
0.454695	−	0.890647i	\(-0.349748\pi\)
\(19\)	4.42397			1.01493			0.507464	−	0.861673i	\(-0.330583\pi\)
							0.507464	+	0.861673i	\(0.330583\pi\)
\(23\)	0.138239	+	0.0798122i	0.0288248	+	0.0166420i	0.514343	−	0.857584i	\(-0.328036\pi\)
							−0.485518	+	0.874226i	\(0.661369\pi\)
\(29\)	−3.73918	+	2.15882i	−0.694349	+	0.400882i	−0.805239	−	0.592950i	\(-0.797963\pi\)
							0.110890	+	0.993833i	\(0.464630\pi\)
\(31\)	2.47099	−	4.27988i	0.443803	−	0.768689i	−0.554165	−	0.832407i	\(-0.686962\pi\)
							0.997968	+	0.0637177i	\(0.0202957\pi\)
\(37\)	4.38451	+	2.53140i	0.720810	+	0.416160i	0.815051	−	0.579390i	\(-0.196709\pi\)
							−0.0942409	+	0.995549i	\(0.530042\pi\)
\(41\)	5.83785	−	3.37048i	0.911718	−	0.526381i	0.0307347	−	0.999528i	\(-0.490215\pi\)
							0.880984	+	0.473147i	\(0.156882\pi\)
\(43\)	2.59600	−	4.49640i	0.395886	−	0.685695i	−0.597328	−	0.801997i	\(-0.703771\pi\)
							0.993214	+	0.116302i	\(0.0371041\pi\)
\(47\)	5.40268	−	3.11924i	0.788062	−	0.454988i	−0.0512176	−	0.998688i	\(-0.516310\pi\)
							0.839280	+	0.543700i	\(0.182977\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.y.b.101.11	✓	64
3.2	odd	2	inner	273.2.y.b.101.22	yes	64
7.5	odd	6		273.2.br.b.257.22	yes	64
13.4	even	6		273.2.br.b.17.11	yes	64
21.5	even	6		273.2.br.b.257.11	yes	64
39.17	odd	6		273.2.br.b.17.22	yes	64
91.82	odd	6	inner	273.2.y.b.173.22	yes	64
273.173	even	6	inner	273.2.y.b.173.11	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.y.b.101.11	✓	64	1.1	even	1	trivial
273.2.y.b.101.22	yes	64	3.2	odd	2	inner
273.2.y.b.173.11	yes	64	273.173	even	6	inner
273.2.y.b.173.22	yes	64	91.82	odd	6	inner
273.2.br.b.17.11	yes	64	13.4	even	6
273.2.br.b.17.22	yes	64	39.17	odd	6
273.2.br.b.257.11	yes	64	21.5	even	6
273.2.br.b.257.22	yes	64	7.5	odd	6