Newform orbit 1176.2.k.b

• Label: 1176.2.k.b
• Level: $1176$
• Weight: $2$
• Character orbit: 1176.k
• Analytic conductor: $9.390$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.k (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.39040727770\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 16 q^{15} + 8 q^{25} + 16 q^{37} - 64 q^{39} + 16 q^{43} + 48 q^{51} + 48 q^{57} + 16 q^{67} + 80 q^{81} - 64 q^{85} - 32 q^{93} - 56 q^{99}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
881.1		0		−1.72171	−	0.188994i		0		4.01535				0			0			0		2.92856	+	0.650785i		0
881.2		0		−1.72171	+	0.188994i		0		4.01535				0			0			0		2.92856	−	0.650785i		0
881.3		0		−1.71558	−	0.238292i		0		−1.32383				0			0			0		2.88643	+	0.817619i		0
881.4		0		−1.71558	+	0.238292i		0		−1.32383				0			0			0		2.88643	−	0.817619i		0
881.5		0		−1.48931	−	0.884275i		0		−0.992103				0			0			0		1.43612	+	2.63393i		0
881.6		0		−1.48931	+	0.884275i		0		−0.992103				0			0			0		1.43612	−	2.63393i		0
881.7		0		−0.698115	−	1.58513i		0		0.489061				0			0			0		−2.02527	+	2.21321i		0
881.8		0		−0.698115	+	1.58513i		0		0.489061				0			0			0		−2.02527	−	2.21321i		0
881.9		0		−0.615077	−	1.61916i		0		1.31193				0			0			0		−2.24336	+	1.99182i		0
881.10		0		−0.615077	+	1.61916i		0		1.31193				0			0			0		−2.24336	−	1.99182i		0
881.11		0		−0.0935860	−	1.72952i		0		−3.34363				0			0			0		−2.98248	+	0.323718i		0
881.12		0		−0.0935860	+	1.72952i		0		−3.34363				0			0			0		−2.98248	−	0.323718i		0
881.13		0		0.0935860	−	1.72952i		0		3.34363				0			0			0		−2.98248	−	0.323718i		0
881.14		0		0.0935860	+	1.72952i		0		3.34363				0			0			0		−2.98248	+	0.323718i		0
881.15		0		0.615077	−	1.61916i		0		−1.31193				0			0			0		−2.24336	−	1.99182i		0
881.16		0		0.615077	+	1.61916i		0		−1.31193				0			0			0		−2.24336	+	1.99182i		0
881.17		0		0.698115	−	1.58513i		0		−0.489061				0			0			0		−2.02527	−	2.21321i		0
881.18		0		0.698115	+	1.58513i		0		−0.489061				0			0			0		−2.02527	+	2.21321i		0
881.19		0		1.48931	−	0.884275i		0		0.992103				0			0			0		1.43612	−	2.63393i		0
881.20		0		1.48931	+	0.884275i		0		0.992103				0			0			0		1.43612	+	2.63393i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
7.b	odd	2	1	inner
21.c	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1176.2.k.b	✓	24
3.b	odd	2	1	inner	1176.2.k.b	✓	24
4.b	odd	2	1		2352.2.k.j		24
7.b	odd	2	1	inner	1176.2.k.b	✓	24
7.c	even	3	2		1176.2.u.c		48
7.d	odd	6	2		1176.2.u.c		48
12.b	even	2	1		2352.2.k.j		24
21.c	even	2	1	inner	1176.2.k.b	✓	24
21.g	even	6	2		1176.2.u.c		48
21.h	odd	6	2		1176.2.u.c		48
28.d	even	2	1		2352.2.k.j		24
84.h	odd	2	1		2352.2.k.j		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1176.2.k.b	✓	24	1.a	even	1	1	trivial
1176.2.k.b	✓	24	3.b	odd	2	1	inner
1176.2.k.b	✓	24	7.b	odd	2	1	inner
1176.2.k.b	✓	24	21.c	even	2	1	inner
1176.2.u.c		48	7.c	even	3	2
1176.2.u.c		48	7.d	odd	6	2
1176.2.u.c		48	21.g	even	6	2
1176.2.u.c		48	21.h	odd	6	2
2352.2.k.j		24	4.b	odd	2	1
2352.2.k.j		24	12.b	even	2	1
2352.2.k.j		24	28.d	even	2	1
2352.2.k.j		24	84.h	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{12} - 32T_{5}^{10} + 316T_{5}^{8} - 1056T_{5}^{6} + 1476T_{5}^{4} - 832T_{5}^{2} + 128 \) acting on \(S_{2}^{\mathrm{new}}(1176, [\chi])\).