Newform orbit 2880.2.bl.c

• Label: 2880.2.bl.c
• Level: $2880$
• Weight: $2$
• Character orbit: 2880.bl
• Analytic conductor: $22.997$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(22.9969157821\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(i)\)
Twist minimal:	no (minimal twist has level 720)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 8 q^{19} - 32 q^{49} + 16 q^{55} + 16 q^{61} - 16 q^{67} + 16 q^{85} + 16 q^{91}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
431.1		0			0			0		−0.707107	−	0.707107i		0		3.01345				0			0			0
431.2		0			0			0		−0.707107	−	0.707107i		0		−3.83891				0			0			0
431.3		0			0			0		−0.707107	−	0.707107i		0		−0.841567				0			0			0
431.4		0			0			0		−0.707107	−	0.707107i		0		−2.45331				0			0			0
431.5		0			0			0		−0.707107	−	0.707107i		0		1.80170				0			0			0
431.6		0			0			0		−0.707107	−	0.707107i		0		−1.44621				0			0			0
431.7		0			0			0		−0.707107	−	0.707107i		0		3.46834				0			0			0
431.8		0			0			0		−0.707107	−	0.707107i		0		0.296505				0			0			0
431.9		0			0			0		0.707107	+	0.707107i		0		3.46834				0			0			0
431.10		0			0			0		0.707107	+	0.707107i		0		−0.841567				0			0			0
431.11		0			0			0		0.707107	+	0.707107i		0		−3.83891				0			0			0
431.12		0			0			0		0.707107	+	0.707107i		0		−1.44621				0			0			0
431.13		0			0			0		0.707107	+	0.707107i		0		3.01345				0			0			0
431.14		0			0			0		0.707107	+	0.707107i		0		1.80170				0			0			0
431.15		0			0			0		0.707107	+	0.707107i		0		−2.45331				0			0			0
431.16		0			0			0		0.707107	+	0.707107i		0		0.296505				0			0			0
1871.1		0			0			0		−0.707107	+	0.707107i		0		3.01345				0			0			0
1871.2		0			0			0		−0.707107	+	0.707107i		0		−3.83891				0			0			0
1871.3		0			0			0		−0.707107	+	0.707107i		0		−0.841567				0			0			0
1871.4		0			0			0		−0.707107	+	0.707107i		0		−2.45331				0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
16.f	odd	4	1	inner
48.k	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.bl.c		32
3.b	odd	2	1	inner	2880.2.bl.c		32
4.b	odd	2	1		720.2.bl.c	✓	32
12.b	even	2	1		720.2.bl.c	✓	32
16.e	even	4	1		720.2.bl.c	✓	32
16.f	odd	4	1	inner	2880.2.bl.c		32
48.i	odd	4	1		720.2.bl.c	✓	32
48.k	even	4	1	inner	2880.2.bl.c		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
720.2.bl.c	✓	32	4.b	odd	2	1
720.2.bl.c	✓	32	12.b	even	2	1
720.2.bl.c	✓	32	16.e	even	4	1
720.2.bl.c	✓	32	48.i	odd	4	1
2880.2.bl.c		32	1.a	even	1	1	trivial
2880.2.bl.c		32	3.b	odd	2	1	inner
2880.2.bl.c		32	16.f	odd	4	1	inner
2880.2.bl.c		32	48.k	even	4	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{8} - 24T_{7}^{6} + 164T_{7}^{4} + 32T_{7}^{3} - 320T_{7}^{2} - 128T_{7} + 64 \) acting on \(S_{2}^{\mathrm{new}}(2880, [\chi])\).