Embedded newform 483.2.y.b.466.8

• Label: 483.2.y.b.466.8
• Level: $483$
• Weight: $2$
• Character: 483.466
• Analytic conductor: $3.857$
• Analytic rank: $0$
• Dimension: $320$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.y (of order \(33\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.85677441763\)
Analytic rank:	\(0\)
Dimension:	\(320\)
Relative dimension:	\(16\) over \(\Q(\zeta_{33})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			466.8
Character	\(\chi\)	\(=\)	483.466
Dual form			483.2.y.b.142.8

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.157854 - 0.0150732i) q^{2} +(0.723734 - 0.690079i) q^{3} +(-1.93917 + 0.373744i) q^{4} +(-1.17091 - 0.603648i) q^{5} +(0.103842 - 0.119841i) q^{6} +(-1.27325 + 2.31923i) q^{7} +(-0.604769 + 0.177576i) q^{8} +(0.0475819 - 0.998867i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 2 q^{2} + 16 q^{3} + 18 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(323\)	\(346\)	\(442\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.157854	−	0.0150732i	0.111620	−	0.0106584i	−0.0390968	−	0.999235i	\(-0.512448\pi\)
							0.150716	+	0.988577i	\(0.451842\pi\)
\(3\)	0.723734	−	0.690079i	0.417848	−	0.398417i
							\(5\)	−1.17091	−	0.603648i	−0.523648	−	0.269960i	0.176071	−	0.984378i	\(-0.443661\pi\)
−0.699719	+	0.714418i	\(0.746692\pi\)
\(7\)	−1.27325	+	2.31923i	−0.481242	+	0.876588i
							\(11\)	3.20215	+	0.305768i	0.965484	+	0.0921926i	0.565873	−	0.824492i	\(-0.308539\pi\)
0.399611	+	0.916685i	\(0.369145\pi\)
\(13\)	0.717504	+	4.99035i	0.199000	+	1.38407i	0.807195	+	0.590286i	\(0.200985\pi\)
							−0.608195	+	0.793788i	\(0.708106\pi\)
\(17\)	0.701700	+	2.02743i	0.170187	+	0.491724i	0.997551	−	0.0699427i	\(-0.0222816\pi\)
							−0.827364	+	0.561666i	\(0.810160\pi\)
\(19\)	−1.87507	+	5.41765i	−0.430170	+	1.24289i	0.496836	+	0.867845i	\(0.334495\pi\)
							−0.927005	+	0.375049i	\(0.877626\pi\)
\(23\)	1.59154	+	4.52405i	0.331859	+	0.943329i
							\(29\)	−6.22697	+	7.18631i	−1.15632	+	1.33446i	−0.223254	+	0.974760i	\(0.571668\pi\)
−0.933066	+	0.359704i	\(0.882878\pi\)
\(31\)	0.842416	−	3.47249i	0.151302	−	0.623677i	−0.844770	−	0.535130i	\(-0.820263\pi\)
							0.996072	−	0.0885469i	\(-0.0282223\pi\)
\(37\)	−0.173658	+	3.64553i	−0.0285492	+	0.599321i	0.938584	+	0.345051i	\(0.112138\pi\)
							−0.967133	+	0.254270i	\(0.918165\pi\)
\(41\)	7.80449	−	5.01564i	1.21886	−	0.783312i	0.236738	−	0.971573i	\(-0.423922\pi\)
							0.982119	+	0.188261i	\(0.0602852\pi\)
\(43\)	−6.63141	−	1.94716i	−1.01128	−	0.296939i	−0.266203	−	0.963917i	\(-0.585769\pi\)
							−0.745077	+	0.666978i	\(0.767587\pi\)
\(47\)	−0.750846	−	1.30050i	−0.109522	−	0.189698i	0.806055	−	0.591841i	\(-0.201599\pi\)
							−0.915577	+	0.402143i	\(0.868265\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.y.b.466.8	yes	320
7.2	even	3	inner	483.2.y.b.121.9	yes	320
23.4	even	11	inner	483.2.y.b.4.9	✓	320
161.142	even	33	inner	483.2.y.b.142.8	yes	320

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.y.b.4.9	✓	320	23.4	even	11	inner
483.2.y.b.121.9	yes	320	7.2	even	3	inner
483.2.y.b.142.8	yes	320	161.142	even	33	inner
483.2.y.b.466.8	yes	320	1.1	even	1	trivial