Newform orbit 1344.4.p.c

• Label: 1344.4.p.c
• Level: $1344$
• Weight: $4$
• Character orbit: 1344.p
• Analytic conductor: $79.299$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1344.p (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(79.2985670477\)
Analytic rank:	\(0\)
Dimension:	\(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 288 q^{9} - 224 q^{13} - 72 q^{21} + 1120 q^{25} - 752 q^{49} - 672 q^{57} - 544 q^{61} + 1536 q^{65} - 144 q^{69} - 1632 q^{77} + 2592 q^{81}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
223.1		0			−	3.00000i		0		−12.5168				0		18.2936	+	2.88837i		0		−9.00000				0
223.2		0				3.00000i		0		−12.5168				0		18.2936	−	2.88837i		0		−9.00000				0
223.3		0			−	3.00000i		0		−12.8225				0		6.32908	−	17.4053i		0		−9.00000				0
223.4		0				3.00000i		0		−12.8225				0		6.32908	+	17.4053i		0		−9.00000				0
223.5		0			−	3.00000i		0		20.7003				0		−11.8166	−	14.2607i		0		−9.00000				0
223.6		0				3.00000i		0		20.7003				0		−11.8166	+	14.2607i		0		−9.00000				0
223.7		0			−	3.00000i		0		−12.5168				0		−18.2936	+	2.88837i		0		−9.00000				0
223.8		0				3.00000i		0		−12.5168				0		−18.2936	−	2.88837i		0		−9.00000				0
223.9		0			−	3.00000i		0		20.7003				0		11.8166	−	14.2607i		0		−9.00000				0
223.10		0				3.00000i		0		20.7003				0		11.8166	+	14.2607i		0		−9.00000				0
223.11		0			−	3.00000i		0		−12.8225				0		−6.32908	−	17.4053i		0		−9.00000				0
223.12		0				3.00000i		0		−12.8225				0		−6.32908	+	17.4053i		0		−9.00000				0
223.13		0			−	3.00000i		0		−15.4018				0		−6.29285	+	17.4184i		0		−9.00000				0
223.14		0				3.00000i		0		−15.4018				0		−6.29285	−	17.4184i		0		−9.00000				0
223.15		0			−	3.00000i		0		1.64166				0		15.2747	+	10.4729i		0		−9.00000				0
223.16		0				3.00000i		0		1.64166				0		15.2747	−	10.4729i		0		−9.00000				0
223.17		0			−	3.00000i		0		5.86484				0		18.3297	−	2.64978i		0		−9.00000				0
223.18		0				3.00000i		0		5.86484				0		18.3297	+	2.64978i		0		−9.00000				0
223.19		0			−	3.00000i		0		−3.15485				0		6.11026	−	17.4833i		0		−9.00000				0
223.20		0				3.00000i		0		−3.15485				0		6.11026	+	17.4833i		0		−9.00000				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
56.e	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	1344.4.p.c	✓	32
4.b	odd	2	1	inner	1344.4.p.c	✓	32
7.b	odd	2	1		1344.4.p.d	yes	32
8.b	even	2	1		1344.4.p.d	yes	32
8.d	odd	2	1		1344.4.p.d	yes	32
28.d	even	2	1		1344.4.p.d	yes	32
56.e	even	2	1	inner	1344.4.p.c	✓	32
56.h	odd	2	1	inner	1344.4.p.c	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1344.4.p.c	✓	32	1.a	even	1	1	trivial
1344.4.p.c	✓	32	4.b	odd	2	1	inner
1344.4.p.c	✓	32	56.e	even	2	1	inner
1344.4.p.c	✓	32	56.h	odd	2	1	inner
1344.4.p.d	yes	32	7.b	odd	2	1
1344.4.p.d	yes	32	8.b	even	2	1
1344.4.p.d	yes	32	8.d	odd	2	1
1344.4.p.d	yes	32	28.d	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{8} - 640T_{5}^{6} - 1728T_{5}^{5} + 116464T_{5}^{4} + 458400T_{5}^{3} - 4875024T_{5}^{2} - 8581632T_{5} + 24385536 \) acting on \(S_{4}^{\mathrm{new}}(1344, [\chi])\).