Newform orbit 3087.2.c.c

• Label: 3087.2.c.c
• Level: $3087$
• Weight: $2$
• Character orbit: 3087.c
• Analytic conductor: $24.650$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3087 = 3^{2} \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3087.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(24.6498191040\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3086.1		−	1.69345i		0		−0.867767			−4.09038				0			0			−	1.91738i		0				6.92685i
3086.2			1.69345i		0		−0.867767			−4.09038				0			0				1.91738i		0			−	6.92685i
3086.3		−	1.98742i		0		−1.94986			3.55325				0			0			−	0.0996578i		0			−	7.06183i
3086.4			1.98742i		0		−1.94986			3.55325				0			0				0.0996578i		0				7.06183i
3086.5		−	0.660558i		0		1.56366			3.37724				0			0			−	2.35401i		0			−	2.23086i
3086.6			0.660558i		0		1.56366			3.37724				0			0				2.35401i		0				2.23086i
3086.7		−	1.06406i		0		0.867767			−3.23675				0			0			−	3.05149i		0				3.44411i
3086.8			1.06406i		0		0.867767			−3.23675				0			0				3.05149i		0			−	3.44411i
3086.9		−	0.223929i		0		1.94986			−3.02565				0			0			−	0.884487i		0				0.677530i
3086.10			0.223929i		0		1.94986			−3.02565				0			0				0.884487i		0			−	0.677530i
3086.11		−	1.88777i		0		−1.56366			1.89903				0			0			−	0.823703i		0			−	3.58493i
3086.12			1.88777i		0		−1.56366			1.89903				0			0				0.823703i		0				3.58493i
3086.13		−	1.88777i		0		−1.56366			−1.89903				0			0			−	0.823703i		0				3.58493i
3086.14			1.88777i		0		−1.56366			−1.89903				0			0				0.823703i		0			−	3.58493i
3086.15		−	0.223929i		0		1.94986			3.02565				0			0			−	0.884487i		0			−	0.677530i
3086.16			0.223929i		0		1.94986			3.02565				0			0				0.884487i		0				0.677530i
3086.17		−	1.06406i		0		0.867767			3.23675				0			0			−	3.05149i		0			−	3.44411i
3086.18			1.06406i		0		0.867767			3.23675				0			0				3.05149i		0				3.44411i
3086.19		−	0.660558i		0		1.56366			−3.37724				0			0			−	2.35401i		0				2.23086i
3086.20			0.660558i		0		1.56366			−3.37724				0			0				2.35401i		0			−	2.23086i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
7.b	odd	2	1	inner
21.c	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3087.2.c.c	✓	24
3.b	odd	2	1	inner	3087.2.c.c	✓	24
7.b	odd	2	1	inner	3087.2.c.c	✓	24
21.c	even	2	1	inner	3087.2.c.c	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
3087.2.c.c	✓	24	1.a	even	1	1	trivial
3087.2.c.c	✓	24	3.b	odd	2	1	inner
3087.2.c.c	✓	24	7.b	odd	2	1	inner
3087.2.c.c	✓	24	21.c	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{12} + 12T_{2}^{10} + 53T_{2}^{8} + 104T_{2}^{6} + 86T_{2}^{4} + 24T_{2}^{2} + 1 \) acting on \(S_{2}^{\mathrm{new}}(3087, [\chi])\).