Embedded newform 483.2.y.a.4.11

• Label: 483.2.y.a.4.11
• Level: $483$
• Weight: $2$
• Character: 483.4
• 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			4.11
Character	\(\chi\)	\(=\)	483.4
Dual form			483.2.y.a.121.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.466737 - 0.655441i) q^{2} +(-0.235759 + 0.971812i) q^{3} +(0.442377 + 1.27816i) q^{4} +(-0.00881404 + 0.185029i) q^{5} +(0.526928 + 0.608107i) q^{6} +(1.59903 - 2.10787i) q^{7} +(2.58833 + 0.760002i) q^{8} +(-0.888835 - 0.458227i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) \)

Character values

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

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.466737	−	0.655441i	0.330033	−	0.463467i	−0.615902	−	0.787823i	\(-0.711208\pi\)
							0.945935	+	0.324356i	\(0.105148\pi\)
\(3\)	−0.235759	+	0.971812i	−0.136115	+	0.561076i
							\(5\)	−0.00881404	+	0.185029i	−0.00394176	+	0.0827477i	−0.999981	−	0.00616724i	\(-0.998037\pi\)
0.996039	+	0.0889149i	\(0.0283399\pi\)
\(7\)	1.59903	−	2.10787i	0.604377	−	0.796699i
							\(11\)	1.88187	+	2.64272i	0.567405	+	0.796809i	0.994201	−	0.107539i	\(-0.0342971\pi\)
−0.426796	+	0.904348i	\(0.640358\pi\)
\(13\)	−0.0720877	+	0.501381i	−0.0199935	+	0.139058i	−0.997373	−	0.0724343i	\(-0.976923\pi\)
							0.977380	+	0.211492i	\(0.0678323\pi\)
\(17\)	−0.392504	+	0.0756489i	−0.0951962	+	0.0183476i	−0.236627	−	0.971601i	\(-0.576042\pi\)
							0.141431	+	0.989948i	\(0.454830\pi\)
\(19\)	−2.40216	−	0.462978i	−0.551092	−	0.106214i	−0.0938991	−	0.995582i	\(-0.529933\pi\)
							−0.457193	+	0.889367i	\(0.651145\pi\)
\(23\)	−1.16371	+	4.65250i	−0.242649	+	0.970114i
							\(29\)	2.98108	+	3.44035i	0.553573	+	0.638857i	0.961712	−	0.274063i	\(-0.0883676\pi\)
−0.408139	+	0.912920i	\(0.633822\pi\)
\(31\)	5.00085	−	4.76830i	0.898179	−	0.856412i	−0.0920656	−	0.995753i	\(-0.529347\pi\)
							0.990244	+	0.139341i	\(0.0444985\pi\)
\(37\)	−7.11895	−	3.67007i	−1.17035	−	0.603357i	−0.240266	−	0.970707i	\(-0.577235\pi\)
							−0.930083	+	0.367351i	\(0.880265\pi\)
\(41\)	2.79630	+	1.79707i	0.436708	+	0.280655i	0.740466	−	0.672094i	\(-0.234605\pi\)
							−0.303758	+	0.952749i	\(0.598241\pi\)
\(43\)	−3.30973	+	0.971823i	−0.504728	+	0.148202i	−0.524177	−	0.851609i	\(-0.675627\pi\)
							0.0194487	+	0.999811i	\(0.493809\pi\)
\(47\)	0.525343	+	0.909920i	0.0766291	+	0.132726i	0.901794	−	0.432167i	\(-0.142251\pi\)
							−0.825164	+	0.564893i	\(0.808918\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.y.a.4.11	✓	320
7.2	even	3	inner	483.2.y.a.142.6	yes	320
23.6	even	11	inner	483.2.y.a.466.6	yes	320
161.121	even	33	inner	483.2.y.a.121.11	yes	320

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.y.a.4.11	✓	320	1.1	even	1	trivial
483.2.y.a.121.11	yes	320	161.121	even	33	inner
483.2.y.a.142.6	yes	320	7.2	even	3	inner
483.2.y.a.466.6	yes	320	23.6	even	11	inner