Newform orbit 368.4.c.b

• Label: 368.4.c.b
• Level: $368$
• Weight: $4$
• Character orbit: 368.c
• Analytic conductor: $21.713$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	368.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(21.7127028821\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 152 q^{9} + 112 q^{13} - 984 q^{25} - 128 q^{29} - 272 q^{41} - 408 q^{49} - 1440 q^{69} - 1568 q^{73} - 400 q^{77} - 1464 q^{81} + 272 q^{85} + 2688 q^{93}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
367.1		0			−	8.48583i		0			−	13.4914i		0		−14.7816				0		−45.0093				0
367.2		0			−	8.48583i		0				13.4914i		0		14.7816				0		−45.0093				0
367.3		0			−	7.93252i		0			−	3.10391i		0		16.8553				0		−35.9249				0
367.4		0			−	7.93252i		0				3.10391i		0		−16.8553				0		−35.9249				0
367.5		0			−	6.77623i		0			−	17.8668i		0		−2.04784				0		−18.9173				0
367.6		0			−	6.77623i		0				17.8668i		0		2.04784				0		−18.9173				0
367.7		0			−	3.69981i		0			−	2.68968i		0		−3.67078				0		13.3114				0
367.8		0			−	3.69981i		0				2.68968i		0		3.67078				0		13.3114				0
367.9		0			−	2.05436i		0			−	5.60258i		0		27.1953				0		22.7796				0
367.10		0			−	2.05436i		0				5.60258i		0		−27.1953				0		22.7796				0
367.11		0			−	1.11337i		0			−	21.1306i		0		26.3847				0		25.7604				0
367.12		0			−	1.11337i		0				21.1306i		0		−26.3847				0		25.7604				0
367.13		0				1.11337i		0			−	21.1306i		0		−26.3847				0		25.7604				0
367.14		0				1.11337i		0				21.1306i		0		26.3847				0		25.7604				0
367.15		0				2.05436i		0			−	5.60258i		0		−27.1953				0		22.7796				0
367.16		0				2.05436i		0				5.60258i		0		27.1953				0		22.7796				0
367.17		0				3.69981i		0			−	2.68968i		0		3.67078				0		13.3114				0
367.18		0				3.69981i		0				2.68968i		0		−3.67078				0		13.3114				0
367.19		0				6.77623i		0			−	17.8668i		0		2.04784				0		−18.9173				0
367.20		0				6.77623i		0				17.8668i		0		−2.04784				0		−18.9173				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
23.b	odd	2	1	inner
92.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	368.4.c.b	✓	24
4.b	odd	2	1	inner	368.4.c.b	✓	24
23.b	odd	2	1	inner	368.4.c.b	✓	24
92.b	even	2	1	inner	368.4.c.b	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
368.4.c.b	✓	24	1.a	even	1	1	trivial
368.4.c.b	✓	24	4.b	odd	2	1	inner
368.4.c.b	✓	24	23.b	odd	2	1	inner
368.4.c.b	✓	24	92.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{12} + 200T_{3}^{10} + 14270T_{3}^{8} + 428000T_{3}^{6} + 4854833T_{3}^{4} + 17406872T_{3}^{2} + 14899600 \) acting on \(S_{4}^{\mathrm{new}}(368, [\chi])\).