Embedded newform 483.2.y.a.151.4

• Label: 483.2.y.a.151.4
• 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			151.4
Character	\(\chi\)	\(=\)	483.151
Dual form			483.2.y.a.16.4

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.461078 + 1.33220i) q^{2} +(0.888835 - 0.458227i) q^{3} +(0.00994599 + 0.00782161i) q^{4} +(3.91624 - 0.373956i) q^{5} +(0.200626 + 1.39538i) q^{6} +(-1.00683 + 2.44669i) q^{7} +(-2.38689 + 1.53396i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.461078	+	1.33220i	−0.326032	+	0.942007i	0.656241	+	0.754551i	\(0.272145\pi\)
							−0.982273	+	0.187456i	\(0.939976\pi\)
\(3\)	0.888835	−	0.458227i	0.513169	−	0.264557i
							\(5\)	3.91624	−	0.373956i	1.75140	−	0.167238i	0.830493	−	0.557029i	\(-0.188059\pi\)
0.920903	+	0.389791i	\(0.127453\pi\)
\(7\)	−1.00683	+	2.44669i	−0.380545	+	0.924763i
							\(11\)	0.718534	+	2.07607i	0.216646	+	0.625958i	0.999990	+	0.00436999i	\(0.00139102\pi\)
−0.783344	+	0.621588i	\(0.786488\pi\)
\(13\)	−2.77780	+	0.815635i	−0.770422	+	0.226216i	−0.643242	−	0.765663i	\(-0.722411\pi\)
							−0.127181	+	0.991880i	\(0.540593\pi\)
\(17\)	−5.91972	−	2.36990i	−1.43574	−	0.574784i	−0.482204	−	0.876059i	\(-0.660164\pi\)
							−0.953537	+	0.301274i	\(0.902588\pi\)
\(19\)	5.31114	−	2.12626i	1.21846	−	0.487797i	0.328789	−	0.944403i	\(-0.393359\pi\)
							0.889669	+	0.456606i	\(0.150935\pi\)
\(23\)	3.80601	+	2.91792i	0.793609	+	0.608428i
							\(29\)	0.814101	+	5.66220i	0.151175	+	1.05144i	0.914255	+	0.405140i	\(0.132777\pi\)
−0.763080	+	0.646304i	\(0.776314\pi\)
\(31\)	−0.517648	−	10.8668i	−0.0929723	−	1.95173i	−0.259617	−	0.965712i	\(-0.583596\pi\)
							0.166644	−	0.986017i	\(-0.446707\pi\)
\(37\)	0.577496	−	0.810980i	0.0949398	−	0.133324i	−0.764374	−	0.644773i	\(-0.776952\pi\)
							0.859314	+	0.511449i	\(0.170891\pi\)
\(41\)	3.70836	−	8.12017i	0.579148	−	1.26816i	−0.362634	−	0.931932i	\(-0.618122\pi\)
							0.941782	−	0.336225i	\(-0.109150\pi\)
\(43\)	−2.57104	−	1.65231i	−0.392080	−	0.251975i	0.329716	−	0.944080i	\(-0.393047\pi\)
							−0.721796	+	0.692105i	\(0.756683\pi\)
\(47\)	−1.20253	−	2.08284i	−0.175407	−	0.303813i	0.764895	−	0.644155i	\(-0.222791\pi\)
							−0.940302	+	0.340341i	\(0.889457\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.y.a.151.4	yes	320
7.2	even	3	inner	483.2.y.a.289.13	yes	320
23.16	even	11	inner	483.2.y.a.361.13	yes	320
161.16	even	33	inner	483.2.y.a.16.4	✓	320

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.y.a.16.4	✓	320	161.16	even	33	inner
483.2.y.a.151.4	yes	320	1.1	even	1	trivial
483.2.y.a.289.13	yes	320	7.2	even	3	inner
483.2.y.a.361.13	yes	320	23.16	even	11	inner