Newform orbit 2880.2.bg.a

• Label: 2880.2.bg.a
• Level: $2880$
• Weight: $2$
• Character orbit: 2880.bg
• Analytic conductor: $22.997$
• Analytic rank: $0$
• Dimension: $96$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.bg (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(22.9969157821\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(48\) over \(\Q(i)\)
Twist minimal:	no (minimal twist has level 720)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1		0			0			0		−2.23555	+	0.0482170i		0		2.70126	−	2.70126i		0			0			0
17.2		0			0			0		−2.23299	−	0.117317i		0		−0.303980	+	0.303980i		0			0			0
17.3		0			0			0		−2.22271	+	0.244063i		0		0.718424	−	0.718424i		0			0			0
17.4		0			0			0		−2.22117	−	0.257710i		0		3.41086	−	3.41086i		0			0			0
17.5		0			0			0		−2.18604	−	0.470363i		0		−0.177389	+	0.177389i		0			0			0
17.6		0			0			0		−2.05344	−	0.885098i		0		−2.95475	+	2.95475i		0			0			0
17.7		0			0			0		−1.95786	+	1.08017i		0		0.362166	−	0.362166i		0			0			0
17.8		0			0			0		−1.95099	+	1.09255i		0		−1.70979	+	1.70979i		0			0			0
17.9		0			0			0		−1.84310	+	1.26609i		0		0.461154	−	0.461154i		0			0			0
17.10		0			0			0		−1.82503	+	1.29201i		0		−2.02860	+	2.02860i		0			0			0
17.11		0			0			0		−1.82168	−	1.29671i		0		2.16011	−	2.16011i		0			0			0
17.12		0			0			0		−1.57418	−	1.58807i		0		−0.639411	+	0.639411i		0			0			0
17.13		0			0			0		−1.41125	−	1.73447i		0		−2.32146	+	2.32146i		0			0			0
17.14		0			0			0		−1.40237	−	1.74165i		0		2.18248	−	2.18248i		0			0			0
17.15		0			0			0		−1.34765	+	1.78433i		0		−3.52140	+	3.52140i		0			0			0
17.16		0			0			0		−1.07871	+	1.95867i		0		1.03362	−	1.03362i		0			0			0
17.17		0			0			0		−1.03889	−	1.98008i		0		−2.57554	+	2.57554i		0			0			0
17.18		0			0			0		−0.948701	−	2.02484i		0		1.06871	−	1.06871i		0			0			0
17.19		0			0			0		−0.897076	+	2.04823i		0		3.15125	−	3.15125i		0			0			0
17.20		0			0			0		−0.859295	+	2.06437i		0		−1.97431	+	1.97431i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
80.t	odd	4	1	inner
240.bf	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2880.2.bg.a		96
3.b	odd	2	1	inner	2880.2.bg.a		96
4.b	odd	2	1		720.2.bg.a	yes	96
5.c	odd	4	1		2880.2.bc.a		96
12.b	even	2	1		720.2.bg.a	yes	96
15.e	even	4	1		2880.2.bc.a		96
16.e	even	4	1		2880.2.bc.a		96
16.f	odd	4	1		720.2.bc.a	✓	96
20.e	even	4	1		720.2.bc.a	✓	96
48.i	odd	4	1		2880.2.bc.a		96
48.k	even	4	1		720.2.bc.a	✓	96
60.l	odd	4	1		720.2.bc.a	✓	96
80.j	even	4	1		720.2.bg.a	yes	96
80.t	odd	4	1	inner	2880.2.bg.a		96
240.bd	odd	4	1		720.2.bg.a	yes	96
240.bf	even	4	1	inner	2880.2.bg.a		96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
720.2.bc.a	✓	96	16.f	odd	4	1
720.2.bc.a	✓	96	20.e	even	4	1
720.2.bc.a	✓	96	48.k	even	4	1
720.2.bc.a	✓	96	60.l	odd	4	1
720.2.bg.a	yes	96	4.b	odd	2	1
720.2.bg.a	yes	96	12.b	even	2	1
720.2.bg.a	yes	96	80.j	even	4	1
720.2.bg.a	yes	96	240.bd	odd	4	1
2880.2.bc.a		96	5.c	odd	4	1
2880.2.bc.a		96	15.e	even	4	1
2880.2.bc.a		96	16.e	even	4	1
2880.2.bc.a		96	48.i	odd	4	1
2880.2.bg.a		96	1.a	even	1	1	trivial
2880.2.bg.a		96	3.b	odd	2	1	inner
2880.2.bg.a		96	80.t	odd	4	1	inner
2880.2.bg.a		96	240.bf	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(2880, [\chi])\).