Embedded newform 483.2.y.a.151.2

• Label: 483.2.y.a.151.2
• Level: $483$
• Weight: $2$
• Character: 483.151
• 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			151.2
Character	\(\chi\)	\(=\)	483.151
Dual form			483.2.y.a.16.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.783498 + 2.26377i) q^{2} +(0.888835 - 0.458227i) q^{3} +(-2.93867 - 2.31100i) q^{4} +(-2.65564 + 0.253583i) q^{5} +(0.340918 + 2.37114i) q^{6} +(-1.79847 - 1.94049i) q^{7} +(3.50353 - 2.25158i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(323\)	\(346\)	\(442\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.783498	+	2.26377i	−0.554017	+	1.60073i	0.225431	+	0.974259i	\(0.427621\pi\)
							−0.779448	+	0.626467i	\(0.784500\pi\)
\(3\)	0.888835	−	0.458227i	0.513169	−	0.264557i
							\(5\)	−2.65564	+	0.253583i	−1.18764	+	0.113406i	−0.670112	−	0.742260i	\(-0.733754\pi\)
−0.517528	+	0.855666i	\(0.673148\pi\)
\(7\)	−1.79847	−	1.94049i	−0.679757	−	0.733437i
							\(11\)	0.421481	+	1.21779i	0.127081	+	0.367177i	0.990537	−	0.137248i	\(-0.0438256\pi\)
−0.863455	+	0.504425i	\(0.831704\pi\)
\(13\)	5.53104	−	1.62406i	1.53403	−	0.450433i	0.597751	−	0.801681i	\(-0.296061\pi\)
							0.936282	+	0.351249i	\(0.114243\pi\)
\(17\)	−1.01153	−	0.404956i	−0.245332	−	0.0982162i	0.245738	−	0.969336i	\(-0.420970\pi\)
							−0.491070	+	0.871120i	\(0.663394\pi\)
\(19\)	3.52611	−	1.41164i	0.808945	−	0.323853i	0.0699388	−	0.997551i	\(-0.477720\pi\)
							0.739006	+	0.673698i	\(0.235295\pi\)
\(23\)	4.79259	−	0.176362i	0.999324	−	0.0367741i
							\(29\)	−0.592854	−	4.12339i	−0.110090	−	0.765695i	−0.967829	−	0.251609i	\(-0.919040\pi\)
0.857739	−	0.514086i	\(-0.171869\pi\)
\(31\)	−0.319146	−	6.69969i	−0.0573202	−	1.20330i	−0.826002	−	0.563668i	\(-0.809390\pi\)
							0.768681	−	0.639632i	\(-0.220913\pi\)
\(37\)	1.30211	−	1.82856i	0.214065	−	0.300613i	−0.693556	−	0.720403i	\(-0.743957\pi\)
							0.907621	+	0.419790i	\(0.137896\pi\)
\(41\)	2.81998	−	6.17490i	0.440407	−	0.964357i	−0.551116	−	0.834429i	\(-0.685798\pi\)
							0.991523	−	0.129929i	\(-0.0414748\pi\)
\(43\)	−3.63034	−	2.33308i	−0.553622	−	0.355791i	0.233724	−	0.972303i	\(-0.424909\pi\)
							−0.787345	+	0.616512i	\(0.788545\pi\)
\(47\)	−6.24387	−	10.8147i	−0.910762	−	1.57749i	−0.812990	−	0.582278i	\(-0.802162\pi\)
							−0.0977722	−	0.995209i	\(-0.531172\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.y.a.151.2	yes	320
7.2	even	3	inner	483.2.y.a.289.15	yes	320
23.16	even	11	inner	483.2.y.a.361.15	yes	320
161.16	even	33	inner	483.2.y.a.16.2	✓	320

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.y.a.16.2	✓	320	161.16	even	33	inner
483.2.y.a.151.2	yes	320	1.1	even	1	trivial
483.2.y.a.289.15	yes	320	7.2	even	3	inner
483.2.y.a.361.15	yes	320	23.16	even	11	inner