Newform orbit 5328.2.e.g

• Label: 5328.2.e.g
• Level: $5328$
• Weight: $2$
• Character orbit: 5328.e
• Analytic conductor: $42.544$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 5328 = 2^{4} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5328.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(42.5442941969\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 16 q^{13} + 24 q^{37} - 16 q^{49} + 48 q^{61} + 48 q^{73} + 56 q^{85} - 8 q^{97}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2591.1		0			0			0			−	3.82584i		0			−	3.07296i		0			0			0
2591.2		0			0			0			−	3.82584i		0				3.07296i		0			0			0
2591.3		0			0			0			−	2.87880i		0			−	1.02706i		0			0			0
2591.4		0			0			0			−	2.87880i		0				1.02706i		0			0			0
2591.5		0			0			0			−	2.18234i		0			−	1.23564i		0			0			0
2591.6		0			0			0			−	2.18234i		0				1.23564i		0			0			0
2591.7		0			0			0			−	1.16614i		0			−	4.00867i		0			0			0
2591.8		0			0			0			−	1.16614i		0				4.00867i		0			0			0
2591.9		0			0			0			−	0.827995i		0			−	4.12813i		0			0			0
2591.10		0			0			0			−	0.827995i		0				4.12813i		0			0			0
2591.11		0			0			0			−	0.517060i		0			−	0.929718i		0			0			0
2591.12		0			0			0			−	0.517060i		0				0.929718i		0			0			0
2591.13		0			0			0				0.517060i		0			−	0.929718i		0			0			0
2591.14		0			0			0				0.517060i		0				0.929718i		0			0			0
2591.15		0			0			0				0.827995i		0			−	4.12813i		0			0			0
2591.16		0			0			0				0.827995i		0				4.12813i		0			0			0
2591.17		0			0			0				1.16614i		0			−	4.00867i		0			0			0
2591.18		0			0			0				1.16614i		0				4.00867i		0			0			0
2591.19		0			0			0				2.18234i		0			−	1.23564i		0			0			0
2591.20		0			0			0				2.18234i		0				1.23564i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
4.b	odd	2	1	inner
12.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	5328.2.e.g	✓	24
3.b	odd	2	1	inner	5328.2.e.g	✓	24
4.b	odd	2	1	inner	5328.2.e.g	✓	24
12.b	even	2	1	inner	5328.2.e.g	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
5328.2.e.g	✓	24	1.a	even	1	1	trivial
5328.2.e.g	✓	24	3.b	odd	2	1	inner
5328.2.e.g	✓	24	4.b	odd	2	1	inner
5328.2.e.g	✓	24	12.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(5328, [\chi])\):

\( T_{5}^{12} + 30T_{5}^{10} + 296T_{5}^{8} + 1152T_{5}^{6} + 1684T_{5}^{4} + 912T_{5}^{2} + 144 \)

\( T_{11}^{12} - 78T_{11}^{10} + 2097T_{11}^{8} - 23544T_{11}^{6} + 103680T_{11}^{4} - 147744T_{11}^{2} + 46656 \)