Embedded newform 483.2.bf.a.145.14

• Label: 483.2.bf.a.145.14
• 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			145.14
Character	\(\chi\)	\(=\)	483.145
Dual form			483.2.bf.a.10.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.175281 - 0.506440i) q^{2} +(0.458227 - 0.888835i) q^{3} +(1.34635 - 1.05878i) q^{4} +(-1.28396 - 0.122604i) q^{5} +(-0.530461 - 0.0762687i) q^{6} +(2.45236 + 0.992951i) q^{7} +(-1.67388 - 1.07574i) q^{8} +(-0.580057 - 0.814576i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.175281	−	0.506440i	−0.123942	−	0.358108i	0.865912	−	0.500197i	\(-0.166739\pi\)
							−0.989854	+	0.142090i	\(0.954618\pi\)
\(3\)	0.458227	−	0.888835i	0.264557	−	0.513169i
							\(5\)	−1.28396	−	0.122604i	−0.574206	−	0.0548301i	−0.196086	−	0.980587i	\(-0.562823\pi\)
−0.378120	+	0.925757i	\(0.623429\pi\)
\(7\)	2.45236	+	0.992951i	0.926903	+	0.375300i
							\(11\)	−3.41543	−	1.18209i	−1.02979	−	0.356414i	−0.240640	−	0.970614i	\(-0.577357\pi\)
−0.789150	+	0.614201i	\(0.789478\pi\)
\(13\)	1.41376	−	4.81481i	0.392105	−	1.33539i	−0.493013	−	0.870022i	\(-0.664105\pi\)
							0.885118	−	0.465366i	\(-0.154077\pi\)
\(17\)	0.881954	−	0.353081i	0.213905	−	0.0856348i	−0.262235	−	0.965004i	\(-0.584460\pi\)
							0.476140	+	0.879369i	\(0.342035\pi\)
\(19\)	3.52161	+	1.40984i	0.807913	+	0.323440i	0.738590	−	0.674155i	\(-0.235492\pi\)
							0.0693229	+	0.997594i	\(0.477916\pi\)
\(23\)	4.33760	+	2.04579i	0.904452	+	0.426576i
							\(29\)	0.260107	−	1.80908i	0.0483006	−	0.335938i	−0.951315	−	0.308220i	\(-0.900267\pi\)
0.999616	−	0.0277183i	\(-0.00882413\pi\)
\(31\)	−6.75160	−	0.321618i	−1.21262	−	0.0577644i	−0.568498	−	0.822684i	\(-0.692475\pi\)
							−0.644125	+	0.764920i	\(0.722778\pi\)
\(37\)	−3.83290	+	2.72940i	−0.630125	+	0.448710i	−0.849974	−	0.526824i	\(-0.823383\pi\)
							0.219850	+	0.975534i	\(0.429443\pi\)
\(41\)	8.00676	−	3.65657i	1.25045	−	0.571060i	0.323491	−	0.946231i	\(-0.395144\pi\)
							0.926955	+	0.375172i	\(0.122416\pi\)
\(43\)	1.83293	+	2.85209i	0.279519	+	0.434939i	0.952418	−	0.304794i	\(-0.0985878\pi\)
							−0.672900	+	0.739734i	\(0.734951\pi\)
\(47\)	3.17773	+	1.83466i	0.463519	+	0.267613i	0.713523	−	0.700632i	\(-0.247098\pi\)
							−0.250004	+	0.968245i	\(0.580432\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bf.a.145.14	yes	640
7.3	odd	6	inner	483.2.bf.a.283.19	yes	640
23.10	odd	22	inner	483.2.bf.a.355.19	yes	640
161.10	even	66	inner	483.2.bf.a.10.14	✓	640

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bf.a.10.14	✓	640	161.10	even	66	inner
483.2.bf.a.145.14	yes	640	1.1	even	1	trivial
483.2.bf.a.283.19	yes	640	7.3	odd	6	inner
483.2.bf.a.355.19	yes	640	23.10	odd	22	inner