Newform orbit 608.2.n.a

• Label: 608.2.n.a
• Level: $608$
• Weight: $2$
• Character orbit: 608.n
• Analytic conductor: $4.855$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	608.n (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.85490444289\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(20\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 16 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
31.1		0		−1.43575	−	2.48679i		0		−1.53816	−	2.66418i		0				4.51201i		0		−2.62274	+	4.54271i		0
31.2		0		−1.35847	−	2.35294i		0		0.965564	+	1.67241i		0				1.21811i		0		−2.19087	+	3.79471i		0
31.3		0		−1.33207	−	2.30722i		0		1.39265	+	2.41215i		0			−	0.297831i		0		−2.04884	+	3.54870i		0
31.4		0		−1.12813	−	1.95397i		0		0.633877	+	1.09791i		0			−	3.90520i		0		−1.04534	+	1.81059i		0
31.5		0		−1.08754	−	1.88367i		0		0.0807857	+	0.139925i		0				4.23285i		0		−0.865482	+	1.49906i		0
31.6		0		−0.919935	−	1.59337i		0		−2.04786	−	3.54700i		0			−	4.31096i		0		−0.192561	+	0.333525i		0
31.7		0		−0.458422	−	0.794010i		0		−1.06924	−	1.85197i		0			−	0.490899i		0		1.07970	−	1.87009i		0
31.8		0		−0.414743	−	0.718355i		0		−0.594676	−	1.03001i		0			−	0.984520i		0		1.15598	−	2.00221i		0
31.9		0		−0.334438	−	0.579264i		0		0.284317	+	0.492451i		0				1.81050i		0		1.27630	−	2.21062i		0
31.10		0		−0.151888	−	0.263077i		0		1.89274	+	3.27832i		0			−	3.13514i		0		1.45386	−	2.51816i		0
31.11		0		0.151888	+	0.263077i		0		1.89274	+	3.27832i		0				3.13514i		0		1.45386	−	2.51816i		0
31.12		0		0.334438	+	0.579264i		0		0.284317	+	0.492451i		0			−	1.81050i		0		1.27630	−	2.21062i		0
31.13		0		0.414743	+	0.718355i		0		−0.594676	−	1.03001i		0				0.984520i		0		1.15598	−	2.00221i		0
31.14		0		0.458422	+	0.794010i		0		−1.06924	−	1.85197i		0				0.490899i		0		1.07970	−	1.87009i		0
31.15		0		0.919935	+	1.59337i		0		−2.04786	−	3.54700i		0				4.31096i		0		−0.192561	+	0.333525i		0
31.16		0		1.08754	+	1.88367i		0		0.0807857	+	0.139925i		0			−	4.23285i		0		−0.865482	+	1.49906i		0
31.17		0		1.12813	+	1.95397i		0		0.633877	+	1.09791i		0				3.90520i		0		−1.04534	+	1.81059i		0
31.18		0		1.33207	+	2.30722i		0		1.39265	+	2.41215i		0				0.297831i		0		−2.04884	+	3.54870i		0
31.19		0		1.35847	+	2.35294i		0		0.965564	+	1.67241i		0			−	1.21811i		0		−2.19087	+	3.79471i		0
31.20		0		1.43575	+	2.48679i		0		−1.53816	−	2.66418i		0			−	4.51201i		0		−2.62274	+	4.54271i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
19.d	odd	6	1	inner
76.f	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	608.2.n.a	✓	40
4.b	odd	2	1	inner	608.2.n.a	✓	40
8.b	even	2	1		1216.2.n.g		40
8.d	odd	2	1		1216.2.n.g		40
19.d	odd	6	1	inner	608.2.n.a	✓	40
76.f	even	6	1	inner	608.2.n.a	✓	40
152.l	odd	6	1		1216.2.n.g		40
152.o	even	6	1		1216.2.n.g		40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
608.2.n.a	✓	40	1.a	even	1	1	trivial
608.2.n.a	✓	40	4.b	odd	2	1	inner
608.2.n.a	✓	40	19.d	odd	6	1	inner
608.2.n.a	✓	40	76.f	even	6	1	inner
1216.2.n.g		40	8.b	even	2	1
1216.2.n.g		40	8.d	odd	2	1
1216.2.n.g		40	152.l	odd	6	1
1216.2.n.g		40	152.o	even	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(608, [\chi])\).