Embedded newform 483.2.bf.a.145.8

• Label: 483.2.bf.a.145.8
• 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			145.8
Character	\(\chi\)	\(=\)	483.145
Dual form			483.2.bf.a.10.8

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.544288 - 1.57262i) q^{2} +(-0.458227 + 0.888835i) q^{3} +(-0.604770 + 0.475596i) q^{4} +(1.92390 + 0.183711i) q^{5} +(1.64721 + 0.236832i) q^{6} +(0.763953 - 2.53306i) q^{7} +(-1.72283 - 1.10720i) q^{8} +(-0.580057 - 0.814576i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.544288	−	1.57262i	−0.384870	−	1.11201i	−0.956559	−	0.291538i	\(-0.905833\pi\)
							0.571689	−	0.820470i	\(-0.306288\pi\)
\(3\)	−0.458227	+	0.888835i	−0.264557	+	0.513169i
							\(5\)	1.92390	+	0.183711i	0.860396	+	0.0821579i	0.515919	−	0.856637i	\(-0.327450\pi\)
0.344476	+	0.938795i	\(0.388056\pi\)
\(7\)	0.763953	−	2.53306i	0.288747	−	0.957405i
							\(11\)	3.76860	+	1.30433i	1.13628	+	0.393269i	0.829497	−	0.558511i	\(-0.188627\pi\)
0.306780	+	0.951780i	\(0.400748\pi\)
\(13\)	−0.663405	+	2.25935i	−0.183996	+	0.626631i	0.814898	+	0.579604i	\(0.196793\pi\)
							−0.998894	+	0.0470270i	\(0.985025\pi\)
\(17\)	3.90548	−	1.56352i	0.947217	−	0.379209i	0.153948	−	0.988079i	\(-0.450801\pi\)
							0.793270	+	0.608870i	\(0.208377\pi\)
\(19\)	−1.75029	−	0.700711i	−0.401544	−	0.160754i	0.162095	−	0.986775i	\(-0.448175\pi\)
							−0.563639	+	0.826021i	\(0.690599\pi\)
\(23\)	1.51901	−	4.54891i	0.316735	−	0.948514i
							\(29\)	1.49969	−	10.4306i	0.278486	−	1.93691i	−0.0653026	−	0.997866i	\(-0.520801\pi\)
0.343789	−	0.939047i	\(-0.388290\pi\)
\(31\)	7.19690	+	0.342831i	1.29260	+	0.0615742i	0.682580	−	0.730810i	\(-0.260858\pi\)
							0.610022	+	0.792385i	\(0.291161\pi\)
\(37\)	−8.71711	+	6.20742i	−1.43308	+	1.02049i	−0.440654	+	0.897677i	\(0.645253\pi\)
							−0.992429	+	0.122817i	\(0.960807\pi\)
\(41\)	2.91207	−	1.32990i	0.454788	−	0.207695i	−0.174831	−	0.984598i	\(-0.555938\pi\)
							0.629620	+	0.776904i	\(0.283211\pi\)
\(43\)	1.00556	+	1.56468i	0.153347	+	0.238612i	0.909424	−	0.415870i	\(-0.136523\pi\)
							−0.756077	+	0.654482i	\(0.772887\pi\)
\(47\)	−5.05862	−	2.92060i	−0.737876	−	0.426013i	0.0834205	−	0.996514i	\(-0.473416\pi\)
							−0.821297	+	0.570502i	\(0.806749\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bf.a.145.8	yes	640
7.3	odd	6	inner	483.2.bf.a.283.25	yes	640
23.10	odd	22	inner	483.2.bf.a.355.25	yes	640
161.10	even	66	inner	483.2.bf.a.10.8	✓	640

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bf.a.10.8	✓	640	161.10	even	66	inner
483.2.bf.a.145.8	yes	640	1.1	even	1	trivial
483.2.bf.a.283.25	yes	640	7.3	odd	6	inner
483.2.bf.a.355.25	yes	640	23.10	odd	22	inner