Newform orbit 2912.2.i.a

• Label: 2912.2.i.a
• Level: $2912$
• Weight: $2$
• Character orbit: 2912.i
• Analytic conductor: $23.252$
• Analytic rank: $0$
• Dimension: $84$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2912 = 2^{5} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2912.i (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(23.2524370686\)
Analytic rank:	\(0\)
Dimension:	\(84\)
Twist minimal:	no (minimal twist has level 728)
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.

\(\operatorname{Tr}(f)(q) = \) \( 84 q - 84 q^{9} + 8 q^{17} + 24 q^{23} + 92 q^{25} + 24 q^{39} - 84 q^{49} - 32 q^{55} - 24 q^{65} + 40 q^{79} + 84 q^{81} + 48 q^{87} + 16 q^{95}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
337.1		0			−	2.77388i		0		4.08827				0				1.00000i		0		−4.69442				0
337.2		0				2.77388i		0		4.08827				0			−	1.00000i		0		−4.69442				0
337.3		0			−	2.65465i		0		3.67757				0			−	1.00000i		0		−4.04717				0
337.4		0				2.65465i		0		3.67757				0				1.00000i		0		−4.04717				0
337.5		0			−	1.24325i		0		−4.24503				0			−	1.00000i		0		1.45434				0
337.6		0				1.24325i		0		−4.24503				0				1.00000i		0		1.45434				0
337.7		0			−	2.60765i		0		−3.65839				0				1.00000i		0		−3.79982				0
337.8		0				2.60765i		0		−3.65839				0			−	1.00000i		0		−3.79982				0
337.9		0			−	3.39926i		0		2.48834				0				1.00000i		0		−8.55495				0
337.10		0				3.39926i		0		2.48834				0			−	1.00000i		0		−8.55495				0
337.11		0			−	1.58847i		0		−3.12702				0				1.00000i		0		0.476774				0
337.12		0				1.58847i		0		−3.12702				0			−	1.00000i		0		0.476774				0
337.13		0			−	0.208275i		0		−3.52272				0				1.00000i		0		2.95662				0
337.14		0				0.208275i		0		−3.52272				0			−	1.00000i		0		2.95662				0
337.15		0			−	3.20622i		0		−1.28006				0				1.00000i		0		−7.27982				0
337.16		0				3.20622i		0		−1.28006				0			−	1.00000i		0		−7.27982				0
337.17		0			−	0.944401i		0		3.13735				0			−	1.00000i		0		2.10811				0
337.18		0				0.944401i		0		3.13735				0				1.00000i		0		2.10811				0
337.19		0			−	2.58827i		0		1.51724				0				1.00000i		0		−3.69913				0
337.20		0				2.58827i		0		1.51724				0			−	1.00000i		0		−3.69913				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.b	even	2	1	inner
13.b	even	2	1	inner
104.e	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2912.2.i.a		84
4.b	odd	2	1		728.2.i.a	✓	84
8.b	even	2	1	inner	2912.2.i.a		84
8.d	odd	2	1		728.2.i.a	✓	84
13.b	even	2	1	inner	2912.2.i.a		84
52.b	odd	2	1		728.2.i.a	✓	84
104.e	even	2	1	inner	2912.2.i.a		84
104.h	odd	2	1		728.2.i.a	✓	84

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
728.2.i.a	✓	84	4.b	odd	2	1
728.2.i.a	✓	84	8.d	odd	2	1
728.2.i.a	✓	84	52.b	odd	2	1
728.2.i.a	✓	84	104.h	odd	2	1
2912.2.i.a		84	1.a	even	1	1	trivial
2912.2.i.a		84	8.b	even	2	1	inner
2912.2.i.a		84	13.b	even	2	1	inner
2912.2.i.a		84	104.e	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(2912, [\chi])\).