Newform orbit 2880.2.bc.a

• Label: 2880.2.bc.a
• Level: $2880$
• Weight: $2$
• Character orbit: 2880.bc
• 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.bc (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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
593.1		0			0			0		−2.23567	+	0.0422885i		0		−1.80532	−	1.80532i		0			0			0
593.2		0			0			0		−2.23368	+	0.103242i		0		−1.05564	−	1.05564i		0			0			0
593.3		0			0			0		−2.21174	+	0.328918i		0		2.33595	+	2.33595i		0			0			0
593.4		0			0			0		−2.14437	−	0.633793i		0		−0.431588	−	0.431588i		0			0			0
593.5		0			0			0		−2.06437	+	0.859295i		0		1.97431	+	1.97431i		0			0			0
593.6		0			0			0		−2.04823	+	0.897076i		0		−3.15125	−	3.15125i		0			0			0
593.7		0			0			0		−2.02484	−	0.948701i		0		−1.06871	−	1.06871i		0			0			0
593.8		0			0			0		−1.98008	−	1.03889i		0		2.57554	+	2.57554i		0			0			0
593.9		0			0			0		−1.95867	+	1.07871i		0		−1.03362	−	1.03362i		0			0			0
593.10		0			0			0		−1.78433	+	1.34765i		0		3.52140	+	3.52140i		0			0			0
593.11		0			0			0		−1.74165	−	1.40237i		0		−2.18248	−	2.18248i		0			0			0
593.12		0			0			0		−1.73447	−	1.41125i		0		2.32146	+	2.32146i		0			0			0
593.13		0			0			0		−1.58807	−	1.57418i		0		0.639411	+	0.639411i		0			0			0
593.14		0			0			0		−1.29671	−	1.82168i		0		−2.16011	−	2.16011i		0			0			0
593.15		0			0			0		−1.29201	+	1.82503i		0		2.02860	+	2.02860i		0			0			0
593.16		0			0			0		−1.26609	+	1.84310i		0		−0.461154	−	0.461154i		0			0			0
593.17		0			0			0		−1.09255	+	1.95099i		0		1.70979	+	1.70979i		0			0			0
593.18		0			0			0		−1.08017	+	1.95786i		0		−0.362166	−	0.362166i		0			0			0
593.19		0			0			0		−0.885098	−	2.05344i		0		2.95475	+	2.95475i		0			0			0
593.20		0			0			0		−0.470363	−	2.18604i		0		0.177389	+	0.177389i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
80.i	odd	4	1	inner
240.bb	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.bc.a		96
3.b	odd	2	1	inner	2880.2.bc.a		96
4.b	odd	2	1		720.2.bc.a	✓	96
5.c	odd	4	1		2880.2.bg.a		96
12.b	even	2	1		720.2.bc.a	✓	96
15.e	even	4	1		2880.2.bg.a		96
16.e	even	4	1		2880.2.bg.a		96
16.f	odd	4	1		720.2.bg.a	yes	96
20.e	even	4	1		720.2.bg.a	yes	96
48.i	odd	4	1		2880.2.bg.a		96
48.k	even	4	1		720.2.bg.a	yes	96
60.l	odd	4	1		720.2.bg.a	yes	96
80.i	odd	4	1	inner	2880.2.bc.a		96
80.s	even	4	1		720.2.bc.a	✓	96
240.z	odd	4	1		720.2.bc.a	✓	96
240.bb	even	4	1	inner	2880.2.bc.a		96

    

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

Hecke kernels

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