Embedded newform 273.2.y.b.101.17

• Label: 273.2.y.b.101.17
• 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			101.17
Character	\(\chi\)	\(=\)	273.101
Dual form			273.2.y.b.173.17

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.0381512 - 0.0660798i) q^{2} +(-1.25975 + 1.18871i) q^{3} +(0.997089 + 1.72701i) q^{4} +(3.58354 - 2.06896i) q^{5} +(0.0304884 + 0.128595i) q^{6} +(-0.269802 - 2.63196i) q^{7} +0.304765 q^{8} +(0.173957 - 2.99495i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 28 q^{4} - 12 q^{7}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.0381512	−	0.0660798i	0.0269770	−	0.0467255i	−0.852222	−	0.523181i	\(-0.824745\pi\)
							0.879199	+	0.476455i	\(0.158079\pi\)
\(3\)	−1.25975	+	1.18871i	−0.727319	+	0.686300i
							\(5\)	3.58354	−	2.06896i	1.60261	−	0.925267i	0.611646	−	0.791132i	\(-0.290508\pi\)
0.990963	−	0.134135i	\(-0.0428255\pi\)
\(7\)	−0.269802	−	2.63196i	−0.101976	−	0.994787i
							\(11\)	−0.0370897			−0.0111830			−0.00559148	−	0.999984i	\(-0.501780\pi\)
−0.00559148	+	0.999984i	\(0.501780\pi\)
\(13\)	2.92881	+	2.10287i	0.812305	+	0.583232i
							\(17\)	1.65944	+	2.87423i	0.402472	+	0.697102i	0.994024	−	0.109165i	\(-0.0348177\pi\)
−0.591552	+	0.806267i	\(0.701484\pi\)
\(19\)	−0.947740			−0.217426			−0.108713	−	0.994073i	\(-0.534673\pi\)
							−0.108713	+	0.994073i	\(0.534673\pi\)
\(23\)	−5.87125	−	3.38977i	−1.22424	−	0.706816i	−0.258422	−	0.966032i	\(-0.583202\pi\)
							−0.965819	+	0.259216i	\(0.916536\pi\)
\(29\)	−2.57400	+	1.48610i	−0.477980	+	0.275962i	−0.719574	−	0.694415i	\(-0.755663\pi\)
							0.241594	+	0.970377i	\(0.422330\pi\)
\(31\)	−3.10288	+	5.37435i	−0.557294	+	0.965262i	0.440427	+	0.897789i	\(0.354827\pi\)
							−0.997721	+	0.0674734i	\(0.978506\pi\)
\(37\)	5.09988	+	2.94442i	0.838415	+	0.484059i	0.856725	−	0.515773i	\(-0.172495\pi\)
							−0.0183103	+	0.999832i	\(0.505829\pi\)
\(41\)	−8.34651	+	4.81886i	−1.30351	+	0.752579i	−0.981004	−	0.193990i	\(-0.937857\pi\)
							−0.322502	+	0.946569i	\(0.604524\pi\)
\(43\)	3.55641	−	6.15988i	0.542347	−	0.939372i	−0.456422	−	0.889763i	\(-0.650869\pi\)
							0.998769	−	0.0496088i	\(-0.0157974\pi\)
\(47\)	2.84334	−	1.64160i	0.414743	−	0.239452i	−0.278082	−	0.960557i	\(-0.589699\pi\)
							0.692826	+	0.721105i	\(0.256366\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.y.b.101.17	yes	64
3.2	odd	2	inner	273.2.y.b.101.16	✓	64
7.5	odd	6		273.2.br.b.257.16	yes	64
13.4	even	6		273.2.br.b.17.17	yes	64
21.5	even	6		273.2.br.b.257.17	yes	64
39.17	odd	6		273.2.br.b.17.16	yes	64
91.82	odd	6	inner	273.2.y.b.173.16	yes	64
273.173	even	6	inner	273.2.y.b.173.17	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.y.b.101.16	✓	64	3.2	odd	2	inner
273.2.y.b.101.17	yes	64	1.1	even	1	trivial
273.2.y.b.173.16	yes	64	91.82	odd	6	inner
273.2.y.b.173.17	yes	64	273.173	even	6	inner
273.2.br.b.17.16	yes	64	39.17	odd	6
273.2.br.b.17.17	yes	64	13.4	even	6
273.2.br.b.257.16	yes	64	7.5	odd	6
273.2.br.b.257.17	yes	64	21.5	even	6