Embedded newform 483.2.bf.a.10.24

• Label: 483.2.bf.a.10.24
• Level: $483$
• Weight: $2$
• Character: 483.10
• 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			10.24
Character	\(\chi\)	\(=\)	483.10
Dual form			483.2.bf.a.145.24

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.541022 - 1.56318i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.578722 - 0.455112i) q^{4} +(-1.66444 + 0.158934i) q^{5} +(1.63732 - 0.235411i) q^{6} +(1.09045 + 2.41059i) q^{7} +(1.75861 - 1.13019i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(323\)	\(346\)	\(442\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{3}{22}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.541022	−	1.56318i	0.382560	−	1.10534i	−0.575261	−	0.817970i	\(-0.695099\pi\)
							0.957821	−	0.287365i	\(-0.0927794\pi\)
\(3\)	0.458227	+	0.888835i	0.264557	+	0.513169i
							\(5\)	−1.66444	+	0.158934i	−0.744359	+	0.0710777i	−0.460342	−	0.887742i	\(-0.652273\pi\)
−0.284017	+	0.958819i	\(0.591667\pi\)
\(7\)	1.09045	+	2.41059i	0.412150	+	0.911116i
							\(11\)	1.58493	−	0.548550i	0.477875	−	0.165394i	−0.0775033	−	0.996992i	\(-0.524695\pi\)
0.555378	+	0.831598i	\(0.312574\pi\)
\(13\)	0.290660	+	0.989898i	0.0806146	+	0.274548i	0.989930	−	0.141560i	\(-0.0452119\pi\)
							−0.909315	+	0.416108i	\(0.863394\pi\)
\(17\)	7.44182	+	2.97926i	1.80491	+	0.722576i	0.989655	+	0.143471i	\(0.0458263\pi\)
							0.815253	+	0.579105i	\(0.196598\pi\)
\(19\)	−1.17674	+	0.471095i	−0.269962	+	0.108077i	−0.502694	−	0.864464i	\(-0.667658\pi\)
							0.232732	+	0.972541i	\(0.425234\pi\)
\(23\)	4.47959	+	1.71269i	0.934058	+	0.357121i
							\(29\)	−1.03896	−	7.22612i	−0.192930	−	1.34186i	−0.824202	−	0.566296i	\(-0.808376\pi\)
0.631272	−	0.775561i	\(-0.282533\pi\)
\(31\)	−0.732534	+	0.0348949i	−0.131567	+	0.00626731i	−0.113262	−	0.993565i	\(-0.536130\pi\)
							−0.0183049	+	0.999832i	\(0.505827\pi\)
\(37\)	2.16985	+	1.54514i	0.356721	+	0.254020i	0.744342	−	0.667799i	\(-0.232763\pi\)
							−0.387620	+	0.921819i	\(0.626703\pi\)
\(41\)	−2.27573	−	1.03929i	−0.355409	−	0.162310i	0.229706	−	0.973260i	\(-0.426223\pi\)
							−0.585115	+	0.810950i	\(0.698951\pi\)
\(43\)	−1.31574	+	2.04733i	−0.200649	+	0.312215i	−0.926967	−	0.375143i	\(-0.877594\pi\)
							0.726318	+	0.687359i	\(0.241230\pi\)
\(47\)	−2.89094	+	1.66908i	−0.421687	+	0.243461i	−0.695799	−	0.718237i	\(-0.744949\pi\)
							0.274112	+	0.961698i	\(0.411616\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bf.a.10.24	✓	640
7.5	odd	6	inner	483.2.bf.a.355.9	yes	640
23.7	odd	22	inner	483.2.bf.a.283.9	yes	640
161.145	even	66	inner	483.2.bf.a.145.24	yes	640

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bf.a.10.24	✓	640	1.1	even	1	trivial
483.2.bf.a.145.24	yes	640	161.145	even	66	inner
483.2.bf.a.283.9	yes	640	23.7	odd	22	inner
483.2.bf.a.355.9	yes	640	7.5	odd	6	inner