Newform orbit 3864.2.u.h

• Label: 3864.2.u.h
• Level: $3864$
• Weight: $2$
• Character orbit: 3864.u
• Analytic conductor: $30.854$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3864.u (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(30.8541953410\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 32 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1609.1		0			−	1.00000i		0		−4.12935				0		1.07448	+	2.41775i		0		−1.00000				0
1609.2		0			−	1.00000i		0		4.12935				0		−1.07448	−	2.41775i		0		−1.00000				0
1609.3		0				1.00000i		0		−4.12935				0		1.07448	−	2.41775i		0		−1.00000				0
1609.4		0				1.00000i		0		4.12935				0		−1.07448	+	2.41775i		0		−1.00000				0
1609.5		0			−	1.00000i		0		−4.15844				0		2.42339	−	1.06170i		0		−1.00000				0
1609.6		0			−	1.00000i		0		4.15844				0		−2.42339	+	1.06170i		0		−1.00000				0
1609.7		0				1.00000i		0		−4.15844				0		2.42339	+	1.06170i		0		−1.00000				0
1609.8		0				1.00000i		0		4.15844				0		−2.42339	−	1.06170i		0		−1.00000				0
1609.9		0			−	1.00000i		0		−1.52599				0		−2.03801	+	1.68716i		0		−1.00000				0
1609.10		0			−	1.00000i		0		1.52599				0		2.03801	−	1.68716i		0		−1.00000				0
1609.11		0				1.00000i		0		−1.52599				0		−2.03801	−	1.68716i		0		−1.00000				0
1609.12		0				1.00000i		0		1.52599				0		2.03801	+	1.68716i		0		−1.00000				0
1609.13		0			−	1.00000i		0		−3.08436				0		0.769888	−	2.53126i		0		−1.00000				0
1609.14		0			−	1.00000i		0		3.08436				0		−0.769888	+	2.53126i		0		−1.00000				0
1609.15		0				1.00000i		0		−3.08436				0		0.769888	+	2.53126i		0		−1.00000				0
1609.16		0				1.00000i		0		3.08436				0		−0.769888	−	2.53126i		0		−1.00000				0
1609.17		0			−	1.00000i		0		−0.0994920				0		2.05824	+	1.66242i		0		−1.00000				0
1609.18		0			−	1.00000i		0		0.0994920				0		−2.05824	−	1.66242i		0		−1.00000				0
1609.19		0				1.00000i		0		−0.0994920				0		2.05824	−	1.66242i		0		−1.00000				0
1609.20		0				1.00000i		0		0.0994920				0		−2.05824	+	1.66242i		0		−1.00000				0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3864.2.u.h	✓	32
7.b	odd	2	1	inner	3864.2.u.h	✓	32
23.b	odd	2	1	inner	3864.2.u.h	✓	32
161.c	even	2	1	inner	3864.2.u.h	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
3864.2.u.h	✓	32	1.a	even	1	1	trivial
3864.2.u.h	✓	32	7.b	odd	2	1	inner
3864.2.u.h	✓	32	23.b	odd	2	1	inner
3864.2.u.h	✓	32	161.c	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{16} - 52T_{5}^{14} + 1002T_{5}^{12} - 8915T_{5}^{10} + 38506T_{5}^{8} - 82412T_{5}^{6} + 81016T_{5}^{4} - 26656T_{5}^{2} + 256 \) acting on \(S_{2}^{\mathrm{new}}(3864, [\chi])\).