Newform orbit 2160.3.c.q

• Label: 2160.3.c.q
• Level: $2160$
• Weight: $3$
• Character orbit: 2160.c
• Analytic conductor: $58.856$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2160.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(58.8557371018\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	no (minimal twist has level 1080)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 72 q^{25} + 72 q^{31} - 408 q^{49} + 168 q^{55} - 240 q^{61} + 312 q^{79} - 96 q^{85}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1889.1		0			0			0		−4.67464	−	1.77419i		0			−	9.67132i		0			0			0
1889.2		0			0			0		−4.67464	+	1.77419i		0				9.67132i		0			0			0
1889.3		0			0			0		−4.52542	−	2.12616i		0				0.343255i		0			0			0
1889.4		0			0			0		−4.52542	+	2.12616i		0			−	0.343255i		0			0			0
1889.5		0			0			0		−4.01139	−	2.98475i		0			−	2.17094i		0			0			0
1889.6		0			0			0		−4.01139	+	2.98475i		0				2.17094i		0			0			0
1889.7		0			0			0		−2.12464	−	4.52614i		0				4.02248i		0			0			0
1889.8		0			0			0		−2.12464	+	4.52614i		0			−	4.02248i		0			0			0
1889.9		0			0			0		−1.72017	−	4.69478i		0				13.6186i		0			0			0
1889.10		0			0			0		−1.72017	+	4.69478i		0			−	13.6186i		0			0			0
1889.11		0			0			0		−0.322433	−	4.98959i		0			−	9.79740i		0			0			0
1889.12		0			0			0		−0.322433	+	4.98959i		0				9.79740i		0			0			0
1889.13		0			0			0		0.322433	−	4.98959i		0				9.79740i		0			0			0
1889.14		0			0			0		0.322433	+	4.98959i		0			−	9.79740i		0			0			0
1889.15		0			0			0		1.72017	−	4.69478i		0			−	13.6186i		0			0			0
1889.16		0			0			0		1.72017	+	4.69478i		0				13.6186i		0			0			0
1889.17		0			0			0		2.12464	−	4.52614i		0			−	4.02248i		0			0			0
1889.18		0			0			0		2.12464	+	4.52614i		0				4.02248i		0			0			0
1889.19		0			0			0		4.01139	−	2.98475i		0				2.17094i		0			0			0
1889.20		0			0			0		4.01139	+	2.98475i		0			−	2.17094i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.b	even	2	1	inner
15.d	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2160.3.c.q		24
3.b	odd	2	1	inner	2160.3.c.q		24
4.b	odd	2	1		1080.3.c.c	✓	24
5.b	even	2	1	inner	2160.3.c.q		24
12.b	even	2	1		1080.3.c.c	✓	24
15.d	odd	2	1	inner	2160.3.c.q		24
20.d	odd	2	1		1080.3.c.c	✓	24
60.h	even	2	1		1080.3.c.c	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1080.3.c.c	✓	24	4.b	odd	2	1
1080.3.c.c	✓	24	12.b	even	2	1
1080.3.c.c	✓	24	20.d	odd	2	1
1080.3.c.c	✓	24	60.h	even	2	1
2160.3.c.q		24	1.a	even	1	1	trivial
2160.3.c.q		24	3.b	odd	2	1	inner
2160.3.c.q		24	5.b	even	2	1	inner
2160.3.c.q		24	15.d	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(2160, [\chi])\):

\( T_{7}^{12} + 396T_{7}^{10} + 52086T_{7}^{8} + 2621876T_{7}^{6} + 38464065T_{7}^{4} + 131476872T_{7}^{2} + 14961424 \)

T17^12 - 2322*T17^10 + 1867761*T17^8 - 616559040*T17^6 + 76935826944*T17^4 - 3210739015680*T17^2 + 39999047270400