Embedded newform 483.2.bf.a.145.11

• Label: 483.2.bf.a.145.11
• 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			145.11
Character	\(\chi\)	\(=\)	483.145
Dual form			483.2.bf.a.10.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.319328 - 0.922636i) q^{2} +(0.458227 - 0.888835i) q^{3} +(0.822819 - 0.647072i) q^{4} +(2.77405 + 0.264890i) q^{5} +(-0.966396 - 0.138947i) q^{6} +(1.16682 - 2.37456i) q^{7} +(-2.50245 - 1.60823i) q^{8} +(-0.580057 - 0.814576i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.319328	−	0.922636i	−0.225799	−	0.652402i	−0.999815	−	0.0192367i	\(-0.993876\pi\)
							0.774016	−	0.633166i	\(-0.218245\pi\)
\(3\)	0.458227	−	0.888835i	0.264557	−	0.513169i
							\(5\)	2.77405	+	0.264890i	1.24059	+	0.118462i	0.694643	−	0.719354i	\(-0.255562\pi\)
0.545951	+	0.837817i	\(0.316168\pi\)
\(7\)	1.16682	−	2.37456i	0.441018	−	0.897498i
							\(11\)	−1.78836	−	0.618957i	−0.539211	−	0.186623i	0.0438695	−	0.999037i	\(-0.486031\pi\)
−0.583080	+	0.812415i	\(0.698153\pi\)
\(13\)	−1.20021	+	4.08754i	−0.332879	+	1.13368i	0.607718	+	0.794153i	\(0.292085\pi\)
							−0.940596	+	0.339527i	\(0.889733\pi\)
\(17\)	1.57904	−	0.632151i	0.382973	−	0.153319i	−0.172184	−	0.985065i	\(-0.555082\pi\)
							0.555157	+	0.831746i	\(0.312658\pi\)
\(19\)	3.37986	+	1.35309i	0.775393	+	0.310420i	0.725399	−	0.688329i	\(-0.241655\pi\)
							0.0499942	+	0.998750i	\(0.484080\pi\)
\(23\)	−1.67869	+	4.49244i	−0.350030	+	0.936738i
							\(29\)	−0.571461	+	3.97460i	−0.106118	+	0.738064i	0.865397	+	0.501086i	\(0.167066\pi\)
−0.971515	+	0.236978i	\(0.923843\pi\)
\(31\)	3.99327	+	0.190223i	0.717212	+	0.0341650i	0.403016	−	0.915193i	\(-0.367962\pi\)
							0.314196	+	0.949358i	\(0.398265\pi\)
\(37\)	5.27961	−	3.75959i	0.867962	−	0.618073i	−0.0568982	−	0.998380i	\(-0.518121\pi\)
							0.924860	+	0.380307i	\(0.124182\pi\)
\(41\)	−6.98182	+	3.18849i	−1.09038	+	0.497959i	−0.877723	−	0.479169i	\(-0.840938\pi\)
							−0.212655	+	0.977127i	\(0.568211\pi\)
\(43\)	−1.81961	−	2.83137i	−0.277488	−	0.431780i	0.674336	−	0.738425i	\(-0.264430\pi\)
							−0.951824	+	0.306645i	\(0.900794\pi\)
\(47\)	−2.22689	−	1.28570i	−0.324825	−	0.187538i	0.328716	−	0.944429i	\(-0.393384\pi\)
							−0.653541	+	0.756891i	\(0.726717\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bf.a.145.11	yes	640
7.3	odd	6	inner	483.2.bf.a.283.22	yes	640
23.10	odd	22	inner	483.2.bf.a.355.22	yes	640
161.10	even	66	inner	483.2.bf.a.10.11	✓	640

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bf.a.10.11	✓	640	161.10	even	66	inner
483.2.bf.a.145.11	yes	640	1.1	even	1	trivial
483.2.bf.a.283.22	yes	640	7.3	odd	6	inner
483.2.bf.a.355.22	yes	640	23.10	odd	22	inner