Newform orbit 2064.2.d.c

• Label: 2064.2.d.c
• Level: $2064$
• Weight: $2$
• Character orbit: 2064.d
• Analytic conductor: $16.481$
• Analytic rank: $0$
• Dimension: $48$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2064 = 2^{4} \cdot 3 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2064.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(16.4811229772\)
Analytic rank:	\(0\)
Dimension:	\(48\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 4 q^{9} - 32 q^{13} - 16 q^{21} - 120 q^{25} - 12 q^{33} + 96 q^{37} + 16 q^{45} - 8 q^{49} + 64 q^{61} + 4 q^{69} - 32 q^{73} - 20 q^{81} - 48 q^{85} + 36 q^{93} - 104 q^{97}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
431.1		0		−1.72564	−	0.148846i		0				0.791562i		0				1.85392i		0		2.95569	+	0.513709i		0
431.2		0		−1.72564	+	0.148846i		0			−	0.791562i		0			−	1.85392i		0		2.95569	−	0.513709i		0
431.3		0		−1.64838	−	0.531834i		0				4.02741i		0			−	1.95918i		0		2.43431	+	1.75333i		0
431.4		0		−1.64838	+	0.531834i		0			−	4.02741i		0				1.95918i		0		2.43431	−	1.75333i		0
431.5		0		−1.64789	−	0.533356i		0			−	2.51710i		0			−	2.52324i		0		2.43106	+	1.75782i		0
431.6		0		−1.64789	+	0.533356i		0				2.51710i		0				2.52324i		0		2.43106	−	1.75782i		0
431.7		0		−1.55462	−	0.763639i		0				3.65502i		0			−	1.22884i		0		1.83371	+	2.37434i		0
431.8		0		−1.55462	+	0.763639i		0			−	3.65502i		0				1.22884i		0		1.83371	−	2.37434i		0
431.9		0		−1.37040	−	1.05925i		0			−	3.53482i		0				3.10629i		0		0.755982	+	2.90319i		0
431.10		0		−1.37040	+	1.05925i		0				3.53482i		0			−	3.10629i		0		0.755982	−	2.90319i		0
431.11		0		−1.25669	−	1.19194i		0				0.347955i		0			−	0.252902i		0		0.158562	+	2.99581i		0
431.12		0		−1.25669	+	1.19194i		0			−	0.347955i		0				0.252902i		0		0.158562	−	2.99581i		0
431.13		0		−1.13086	−	1.31192i		0			−	2.97144i		0				1.05169i		0		−0.442291	+	2.96722i		0
431.14		0		−1.13086	+	1.31192i		0				2.97144i		0			−	1.05169i		0		−0.442291	−	2.96722i		0
431.15		0		−0.897165	−	1.48159i		0				2.51704i		0				4.79866i		0		−1.39019	+	2.65845i		0
431.16		0		−0.897165	+	1.48159i		0			−	2.51704i		0			−	4.79866i		0		−1.39019	−	2.65845i		0
431.17		0		−0.854849	−	1.50640i		0				1.49940i		0			−	3.27718i		0		−1.53847	+	2.57548i		0
431.18		0		−0.854849	+	1.50640i		0			−	1.49940i		0				3.27718i		0		−1.53847	−	2.57548i		0
431.19		0		−0.446389	−	1.67354i		0			−	2.52899i		0			−	0.801658i		0		−2.60147	+	1.49410i		0
431.20		0		−0.446389	+	1.67354i		0				2.52899i		0				0.801658i		0		−2.60147	−	1.49410i		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	2064.2.d.c	✓	48
3.b	odd	2	1	inner	2064.2.d.c	✓	48
4.b	odd	2	1	inner	2064.2.d.c	✓	48
12.b	even	2	1	inner	2064.2.d.c	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2064.2.d.c	✓	48	1.a	even	1	1	trivial
2064.2.d.c	✓	48	3.b	odd	2	1	inner
2064.2.d.c	✓	48	4.b	odd	2	1	inner
2064.2.d.c	✓	48	12.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 + 90*T5^22 + 3540*T5^20 + 79988*T5^18 + 1147916*T5^16 + 10920822*T5^14 + 69761797*T5^12 + 296405372*T5^10 + 810927196*T5^8 + 1340303112*T5^6 + 1188123732*T5^4 + 438659712*T5^2 + 37905408