Embedded newform 273.2.u.c.62.7

• Label: 273.2.u.c.62.7
• Level: $273$
• Weight: $2$
• Character: 273.62
• Analytic conductor: $2.180$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.u (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			62.7
Character	\(\chi\)	\(=\)	273.62
Dual form			273.2.u.c.251.7

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.879183 - 1.52279i) q^{2} +(-1.61457 - 0.627032i) q^{3} +(-0.545926 + 0.945572i) q^{4} -0.0518379i q^{5} +(0.464663 + 3.00992i) q^{6} +(-1.90128 + 1.83988i) q^{7} -1.59686 q^{8} +(2.21366 + 2.02477i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 40 q^{4} - 6 q^{9}+O(q^{10}) \)

Character values

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

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.879183	−	1.52279i	−0.621676	−	1.07678i	−0.989174	−	0.146750i	\(-0.953119\pi\)
							0.367497	−	0.930025i	\(-0.380215\pi\)
\(3\)	−1.61457	−	0.627032i	−0.932171	−	0.362017i
							\(5\)		−	0.0518379i		−	0.0231826i	−0.999933	−	0.0115913i	\(-0.996310\pi\)
0.999933	−	0.0115913i	\(-0.00368971\pi\)
\(7\)	−1.90128	+	1.83988i	−0.718615	+	0.695408i
							\(11\)	−0.619047	−	1.07222i	−0.186650	−	0.323287i	0.757482	−	0.652857i	\(-0.226430\pi\)
−0.944131	+	0.329570i	\(0.893096\pi\)
\(13\)	−1.91240	+	3.05659i	−0.530403	+	0.847746i
							\(17\)	−2.53079	+	4.38346i	−0.613808	+	1.06315i	0.376785	+	0.926301i	\(0.377030\pi\)
−0.990592	+	0.136845i	\(0.956304\pi\)
\(19\)	1.58871	−	2.75173i	0.364475	−	0.631289i	−0.624217	−	0.781251i	\(-0.714582\pi\)
							0.988692	+	0.149962i	\(0.0479151\pi\)
\(23\)	3.57137	−	2.06193i	0.744681	−	0.429942i	−0.0790877	−	0.996868i	\(-0.525201\pi\)
							0.823769	+	0.566926i	\(0.191867\pi\)
\(29\)	−8.51613	+	4.91679i	−1.58141	+	0.913025i	−0.586752	+	0.809767i	\(0.699594\pi\)
							−0.994655	+	0.103258i	\(0.967073\pi\)
\(31\)	3.16800			0.568990			0.284495	−	0.958678i	\(-0.408174\pi\)
							0.284495	+	0.958678i	\(0.408174\pi\)
\(37\)	−6.66784	+	3.84968i	−1.09619	+	0.632884i	−0.935217	−	0.354076i	\(-0.884796\pi\)
							−0.160970	+	0.986959i	\(0.551462\pi\)
\(41\)	−5.00308	+	2.88853i	−0.781350	+	0.451112i	−0.836908	−	0.547343i	\(-0.815639\pi\)
							0.0555588	+	0.998455i	\(0.482306\pi\)
\(43\)	−5.05026	+	8.74731i	−0.770158	+	1.33395i	0.167319	+	0.985903i	\(0.446489\pi\)
							−0.937476	+	0.348049i	\(0.886844\pi\)
\(47\)		−	1.44076i		−	0.210156i	−0.994464	−	0.105078i	\(-0.966491\pi\)
							0.994464	−	0.105078i	\(-0.0335093\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.u.c.62.7	✓	64
3.2	odd	2	inner	273.2.u.c.62.25	yes	64
7.6	odd	2	inner	273.2.u.c.62.8	yes	64
13.4	even	6	inner	273.2.u.c.251.26	yes	64
21.20	even	2	inner	273.2.u.c.62.26	yes	64
39.17	odd	6	inner	273.2.u.c.251.8	yes	64
91.69	odd	6	inner	273.2.u.c.251.25	yes	64
273.251	even	6	inner	273.2.u.c.251.7	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.u.c.62.7	✓	64	1.1	even	1	trivial
273.2.u.c.62.8	yes	64	7.6	odd	2	inner
273.2.u.c.62.25	yes	64	3.2	odd	2	inner
273.2.u.c.62.26	yes	64	21.20	even	2	inner
273.2.u.c.251.7	yes	64	273.251	even	6	inner
273.2.u.c.251.8	yes	64	39.17	odd	6	inner
273.2.u.c.251.25	yes	64	91.69	odd	6	inner
273.2.u.c.251.26	yes	64	13.4	even	6	inner