Embedded newform 483.2.bf.a.145.16

• Label: 483.2.bf.a.145.16
• Level: $483$
• Weight: $2$
• Character: 483.145
• Analytic conductor: $3.857$
• Analytic rank: $0$
• Dimension: $640$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bf (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.85677441763\)
Analytic rank:	\(0\)
Dimension:	\(640\)
Relative dimension:	\(32\) over \(\Q(\zeta_{66})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			145.16
Character	\(\chi\)	\(=\)	483.145
Dual form			483.2.bf.a.10.16

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.0815859 - 0.235727i) q^{2} +(-0.458227 + 0.888835i) q^{3} +(1.52320 - 1.19785i) q^{4} +(-1.53664 - 0.146731i) q^{5} +(0.246907 + 0.0354999i) q^{6} +(-2.59838 + 0.498437i) q^{7} +(-0.826333 - 0.531052i) q^{8} +(-0.580057 - 0.814576i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\)	\(323\)	\(346\)	\(442\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{22}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.0815859	−	0.235727i	−0.0576900	−	0.166684i	0.912474	−	0.409136i	\(-0.134170\pi\)
							−0.970164	+	0.242451i	\(0.922049\pi\)
\(3\)	−0.458227	+	0.888835i	−0.264557	+	0.513169i
							\(5\)	−1.53664	−	0.146731i	−0.687206	−	0.0656203i	−0.254389	−	0.967102i	\(-0.581874\pi\)
−0.432817	+	0.901482i	\(0.642480\pi\)
\(7\)	−2.59838	+	0.498437i	−0.982094	+	0.188392i
							\(11\)	3.95026	+	1.36720i	1.19105	+	0.412225i	0.849474	−	0.527630i	\(-0.176919\pi\)
0.341572	+	0.939855i	\(0.389041\pi\)
\(13\)	1.89945	−	6.46894i	0.526813	−	1.79416i	−0.0769940	−	0.997032i	\(-0.524532\pi\)
							0.603807	−	0.797130i	\(-0.293650\pi\)
\(17\)	7.55462	−	3.02441i	1.83226	−	0.733528i	0.855988	−	0.516996i	\(-0.172950\pi\)
							0.976275	−	0.216532i	\(-0.0694746\pi\)
\(19\)	−5.56282	−	2.22702i	−1.27620	−	0.510913i	−0.368145	−	0.929768i	\(-0.620007\pi\)
							−0.908053	+	0.418856i	\(0.862431\pi\)
\(23\)	4.68024	+	1.04661i	0.975897	+	0.218233i
							\(29\)	0.253958	−	1.76632i	0.0471588	−	0.327997i	−0.952562	−	0.304346i	\(-0.901562\pi\)
0.999720	−	0.0236504i	\(-0.00752886\pi\)
\(31\)	−2.00883	−	0.0956922i	−0.360796	−	0.0171868i	−0.133598	−	0.991036i	\(-0.542653\pi\)
							−0.227197	+	0.973849i	\(0.572956\pi\)
\(37\)	6.53454	−	4.65323i	1.07427	−	0.764986i	0.101057	−	0.994881i	\(-0.467778\pi\)
							0.973215	+	0.229895i	\(0.0738382\pi\)
\(41\)	−10.9516	+	5.00143i	−1.71035	+	0.781092i	−0.713602	+	0.700551i	\(0.752938\pi\)
							−0.996751	+	0.0805410i	\(0.974335\pi\)
\(43\)	2.41501	+	3.75782i	0.368285	+	0.573063i	0.975096	−	0.221784i	\(-0.0711878\pi\)
							−0.606811	+	0.794846i	\(0.707551\pi\)
\(47\)	−1.54737	−	0.893376i	−0.225708	−	0.130312i	0.382883	−	0.923797i	\(-0.374931\pi\)
							−0.608590	+	0.793485i	\(0.708265\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bf.a.145.16	yes	640
7.3	odd	6	inner	483.2.bf.a.283.17	yes	640
23.10	odd	22	inner	483.2.bf.a.355.17	yes	640
161.10	even	66	inner	483.2.bf.a.10.16	✓	640

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bf.a.10.16	✓	640	161.10	even	66	inner
483.2.bf.a.145.16	yes	640	1.1	even	1	trivial
483.2.bf.a.283.17	yes	640	7.3	odd	6	inner
483.2.bf.a.355.17	yes	640	23.10	odd	22	inner