Newform orbit 7488.2.j.c

• Label: 7488.2.j.c
• Level: $7488$
• Weight: $2$
• Character orbit: 7488.j
• Analytic conductor: $59.792$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 7488 = 2^{6} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7488.j (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(59.7919810335\)
Analytic rank:	\(0\)
Dimension:	\(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
287.1		0			0			0		−4.42861				0			−	3.42219i		0			0			0
287.2		0			0			0		−4.42861				0				3.42219i		0			0			0
287.3		0			0			0		−3.11042				0				1.74293i		0			0			0
287.4		0			0			0		−3.11042				0			−	1.74293i		0			0			0
287.5		0			0			0		−2.71368				0				2.63603i		0			0			0
287.6		0			0			0		−2.71368				0			−	2.63603i		0			0			0
287.7		0			0			0		−2.13579				0				4.89318i		0			0			0
287.8		0			0			0		−2.13579				0			−	4.89318i		0			0			0
287.9		0			0			0		−1.98073				0				1.05338i		0			0			0
287.10		0			0			0		−1.98073				0			−	1.05338i		0			0			0
287.11		0			0			0		−1.64356				0			−	1.40102i		0			0			0
287.12		0			0			0		−1.64356				0				1.40102i		0			0			0
287.13		0			0			0		−0.366352				0			−	4.57303i		0			0			0
287.14		0			0			0		−0.366352				0				4.57303i		0			0			0
287.15		0			0			0		−0.168038				0				1.54075i		0			0			0
287.16		0			0			0		−0.168038				0			−	1.54075i		0			0			0
287.17		0			0			0		0.168038				0				1.54075i		0			0			0
287.18		0			0			0		0.168038				0			−	1.54075i		0			0			0
287.19		0			0			0		0.366352				0			−	4.57303i		0			0			0
287.20		0			0			0		0.366352				0				4.57303i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
8.d	odd	2	1	inner
24.f	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	7488.2.j.c	✓	32
3.b	odd	2	1	inner	7488.2.j.c	✓	32
4.b	odd	2	1		7488.2.j.d	yes	32
8.b	even	2	1		7488.2.j.d	yes	32
8.d	odd	2	1	inner	7488.2.j.c	✓	32
12.b	even	2	1		7488.2.j.d	yes	32
24.f	even	2	1	inner	7488.2.j.c	✓	32
24.h	odd	2	1		7488.2.j.d	yes	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
7488.2.j.c	✓	32	1.a	even	1	1	trivial
7488.2.j.c	✓	32	3.b	odd	2	1	inner
7488.2.j.c	✓	32	8.d	odd	2	1	inner
7488.2.j.c	✓	32	24.f	even	2	1	inner
7488.2.j.d	yes	32	4.b	odd	2	1
7488.2.j.d	yes	32	8.b	even	2	1
7488.2.j.d	yes	32	12.b	even	2	1
7488.2.j.d	yes	32	24.h	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(7488, [\chi])\):

\( T_{5}^{16} - 48T_{5}^{14} + 864T_{5}^{12} - 7616T_{5}^{10} + 35168T_{5}^{8} - 82176T_{5}^{6} + 80128T_{5}^{4} - 11264T_{5}^{2} + 256 \)

\( T_{19}^{8} + 4T_{19}^{7} - 44T_{19}^{6} - 168T_{19}^{5} + 456T_{19}^{4} + 1296T_{19}^{3} - 1872T_{19}^{2} - 864T_{19} + 864 \)