Newform orbit 5328.2.e.f

• Label: 5328.2.e.f
• 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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 32 q^{25} - 24 q^{37} - 80 q^{49} - 48 q^{61} - 48 q^{73} - 40 q^{85} + 24 q^{97}+O(q^{100}) \)

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			−	3.80589i		0			−	3.34969i		0			0			0
2591.2		0			0			0			−	3.80589i		0				3.34969i		0			0			0
2591.3		0			0			0			−	3.05740i		0			−	1.35466i		0			0			0
2591.4		0			0			0			−	3.05740i		0				1.35466i		0			0			0
2591.5		0			0			0			−	2.80927i		0			−	4.99414i		0			0			0
2591.6		0			0			0			−	2.80927i		0				4.99414i		0			0			0
2591.7		0			0			0			−	2.30074i		0			−	4.07997i		0			0			0
2591.8		0			0			0			−	2.30074i		0				4.07997i		0			0			0
2591.9		0			0			0			−	0.774903i		0			−	1.59995i		0			0			0
2591.10		0			0			0			−	0.774903i		0				1.59995i		0			0			0
2591.11		0			0			0			−	0.617709i		0			−	2.19022i		0			0			0
2591.12		0			0			0			−	0.617709i		0				2.19022i		0			0			0
2591.13		0			0			0				0.617709i		0			−	2.19022i		0			0			0
2591.14		0			0			0				0.617709i		0				2.19022i		0			0			0
2591.15		0			0			0				0.774903i		0			−	1.59995i		0			0			0
2591.16		0			0			0				0.774903i		0				1.59995i		0			0			0
2591.17		0			0			0				2.30074i		0			−	4.07997i		0			0			0
2591.18		0			0			0				2.30074i		0				4.07997i		0			0			0
2591.19		0			0			0				2.80927i		0			−	4.99414i		0			0			0
2591.20		0			0			0				2.80927i		0				4.99414i		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.f	✓	24
3.b	odd	2	1	inner	5328.2.e.f	✓	24
4.b	odd	2	1	inner	5328.2.e.f	✓	24
12.b	even	2	1	inner	5328.2.e.f	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
5328.2.e.f	✓	24	1.a	even	1	1	trivial
5328.2.e.f	✓	24	3.b	odd	2	1	inner
5328.2.e.f	✓	24	4.b	odd	2	1	inner
5328.2.e.f	✓	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 \(S_{2}^{\mathrm{new}}(5328, [\chi])\):

\( T_{5}^{12} + 38T_{5}^{10} + 528T_{5}^{8} + 3272T_{5}^{6} + 8500T_{5}^{4} + 6192T_{5}^{2} + 1296 \)

\( T_{11}^{12} - 62T_{11}^{10} + 1409T_{11}^{8} - 15128T_{11}^{6} + 79712T_{11}^{4} - 183200T_{11}^{2} + 107584 \)