Newform orbit 483.3.g.a

• Label: 483.3.g.a
• Level: $483$
• Weight: $3$
• Character orbit: 483.g
• Analytic conductor: $13.161$
• Analytic rank: $0$
• Dimension: $60$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(13.1607967686\)
Analytic rank:	\(0\)
Dimension:	\(60\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 60q + 128q^{4} - 16q^{7} + 24q^{8} - 180q^{9} + O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
139.1	−3.94080					1.73205i	11.5299					1.76571i		−	6.82566i	−5.04591	−	4.85168i	−29.6737			−3.00000				−	6.95831i
139.2	−3.94080				−	1.73205i	11.5299				−	1.76571i			6.82566i	−5.04591	+	4.85168i	−29.6737			−3.00000					6.95831i
139.3	−3.48909					1.73205i	8.17374				−	1.46096i		−	6.04328i	6.91536	−	1.08528i	−14.5626			−3.00000					5.09743i
139.4	−3.48909				−	1.73205i	8.17374					1.46096i			6.04328i	6.91536	+	1.08528i	−14.5626			−3.00000				−	5.09743i
139.5	−3.29495					1.73205i	6.85669				−	6.17562i		−	5.70702i	−6.91716	+	1.07376i	−9.41266			−3.00000					20.3484i
139.6	−3.29495				−	1.73205i	6.85669					6.17562i			5.70702i	−6.91716	−	1.07376i	−9.41266			−3.00000				−	20.3484i
139.7	−3.28514					1.73205i	6.79214					3.80523i		−	5.69003i	−0.993207	+	6.92918i	−9.17258			−3.00000				−	12.5007i
139.8	−3.28514				−	1.73205i	6.79214				−	3.80523i			5.69003i	−0.993207	−	6.92918i	−9.17258			−3.00000					12.5007i
139.9	−3.13389					1.73205i	5.82124					7.50145i		−	5.42805i	4.32864	−	5.50117i	−5.70757			−3.00000				−	23.5087i
139.10	−3.13389				−	1.73205i	5.82124				−	7.50145i			5.42805i	4.32864	+	5.50117i	−5.70757			−3.00000					23.5087i
139.11	−2.79612					1.73205i	3.81828					8.09762i		−	4.84302i	−5.87622	+	3.80395i	0.508111			−3.00000				−	22.6419i
139.12	−2.79612				−	1.73205i	3.81828				−	8.09762i			4.84302i	−5.87622	−	3.80395i	0.508111			−3.00000					22.6419i
139.13	−2.51134				−	1.73205i	2.30684					3.95129i			4.34977i	−0.923197	+	6.93885i	4.25211			−3.00000				−	9.92304i
139.14	−2.51134					1.73205i	2.30684				−	3.95129i		−	4.34977i	−0.923197	−	6.93885i	4.25211			−3.00000					9.92304i
139.15	−2.20043				−	1.73205i	0.841896					0.777779i			3.81126i	2.99585	−	6.32652i	6.94919			−3.00000				−	1.71145i
139.16	−2.20043					1.73205i	0.841896				−	0.777779i		−	3.81126i	2.99585	+	6.32652i	6.94919			−3.00000					1.71145i
139.17	−2.01661				−	1.73205i	0.0667068					2.33922i			3.49287i	−5.55691	+	4.25685i	7.93191			−3.00000				−	4.71728i
139.18	−2.01661					1.73205i	0.0667068				−	2.33922i		−	3.49287i	−5.55691	−	4.25685i	7.93191			−3.00000					4.71728i
139.19	−1.79815					1.73205i	−0.766656				−	9.01598i		−	3.11449i	6.86887	−	1.34858i	8.57116			−3.00000					16.2121i
139.20	−1.79815				−	1.73205i	−0.766656					9.01598i			3.11449i	6.86887	+	1.34858i	8.57116			−3.00000				−	16.2121i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	483.3.g.a	✓	60
7.b	odd	2	1	inner	483.3.g.a	✓	60

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
483.3.g.a	✓	60	1.a	even	1	1	trivial
483.3.g.a	✓	60	7.b	odd	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(483, [\chi])\).