Newform orbit 4704.2.c.g

• Label: 4704.2.c.g
• Level: $4704$
• Weight: $2$
• Character orbit: 4704.c
• Analytic conductor: $37.562$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 4704 = 2^{5} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4704.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(37.5616291108\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	no (minimal twist has level 1176)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2353.1		0			−	1.00000i		0			−	4.04911i		0			0			0		−1.00000				0
2353.2		0			−	1.00000i		0			−	4.04911i		0			0			0		−1.00000				0
2353.3		0			−	1.00000i		0			−	3.32253i		0			0			0		−1.00000				0
2353.4		0			−	1.00000i		0			−	3.32253i		0			0			0		−1.00000				0
2353.5		0			−	1.00000i		0			−	0.867090i		0			0			0		−1.00000				0
2353.6		0			−	1.00000i		0			−	0.867090i		0			0			0		−1.00000				0
2353.7		0			−	1.00000i		0				0.379866i		0			0			0		−1.00000				0
2353.8		0			−	1.00000i		0				0.379866i		0			0			0		−1.00000				0
2353.9		0			−	1.00000i		0				1.59482i		0			0			0		−1.00000				0
2353.10		0			−	1.00000i		0				1.59482i		0			0			0		−1.00000				0
2353.11		0			−	1.00000i		0				2.26404i		0			0			0		−1.00000				0
2353.12		0			−	1.00000i		0				2.26404i		0			0			0		−1.00000				0
2353.13		0				1.00000i		0			−	2.26404i		0			0			0		−1.00000				0
2353.14		0				1.00000i		0			−	2.26404i		0			0			0		−1.00000				0
2353.15		0				1.00000i		0			−	1.59482i		0			0			0		−1.00000				0
2353.16		0				1.00000i		0			−	1.59482i		0			0			0		−1.00000				0
2353.17		0				1.00000i		0			−	0.379866i		0			0			0		−1.00000				0
2353.18		0				1.00000i		0			−	0.379866i		0			0			0		−1.00000				0
2353.19		0				1.00000i		0				0.867090i		0			0			0		−1.00000				0
2353.20		0				1.00000i		0				0.867090i		0			0			0		−1.00000				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
8.b	even	2	1	inner
56.h	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	4704.2.c.g		24
4.b	odd	2	1		1176.2.c.g	✓	24
7.b	odd	2	1	inner	4704.2.c.g		24
8.b	even	2	1	inner	4704.2.c.g		24
8.d	odd	2	1		1176.2.c.g	✓	24
28.d	even	2	1		1176.2.c.g	✓	24
56.e	even	2	1		1176.2.c.g	✓	24
56.h	odd	2	1	inner	4704.2.c.g		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1176.2.c.g	✓	24	4.b	odd	2	1
1176.2.c.g	✓	24	8.d	odd	2	1
1176.2.c.g	✓	24	28.d	even	2	1
1176.2.c.g	✓	24	56.e	even	2	1
4704.2.c.g		24	1.a	even	1	1	trivial
4704.2.c.g		24	7.b	odd	2	1	inner
4704.2.c.g		24	8.b	even	2	1	inner
4704.2.c.g		24	56.h	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 \(S_{2}^{\mathrm{new}}(4704, [\chi])\):

\( T_{5}^{12} + 36T_{5}^{10} + 436T_{5}^{8} + 2112T_{5}^{6} + 3968T_{5}^{4} + 2304T_{5}^{2} + 256 \)

\( T_{17}^{12} - 76T_{17}^{10} + 2068T_{17}^{8} - 23808T_{17}^{6} + 105216T_{17}^{4} - 140544T_{17}^{2} + 30976 \)