Newform orbit 1456.2.v.b

• Label: 1456.2.v.b
• Level: $1456$
• Weight: $2$
• Character orbit: 1456.v
• Analytic conductor: $11.626$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.v (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.6262185343\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 4 q^{5} - 28 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
239.1		0			−	3.34181i		0		0.187487	−	0.187487i		0		−0.707107	+	0.707107i		0		−8.16768				0
239.2		0			−	2.18785i		0		2.52084	−	2.52084i		0		0.707107	−	0.707107i		0		−1.78667				0
239.3		0			−	2.11240i		0		1.47517	−	1.47517i		0		−0.707107	+	0.707107i		0		−1.46224				0
239.4		0			−	2.07330i		0		−0.828843	+	0.828843i		0		0.707107	−	0.707107i		0		−1.29857				0
239.5		0			−	1.53405i		0		−2.65155	+	2.65155i		0		−0.707107	+	0.707107i		0		0.646698				0
239.6		0			−	0.731249i		0		−1.91599	+	1.91599i		0		−0.707107	+	0.707107i		0		2.46528				0
239.7		0			−	0.629933i		0		0.212889	−	0.212889i		0		0.707107	−	0.707107i		0		2.60318				0
239.8		0				0.629933i		0		0.212889	−	0.212889i		0		−0.707107	+	0.707107i		0		2.60318				0
239.9		0				0.731249i		0		−1.91599	+	1.91599i		0		0.707107	−	0.707107i		0		2.46528				0
239.10		0				1.53405i		0		−2.65155	+	2.65155i		0		0.707107	−	0.707107i		0		0.646698				0
239.11		0				2.07330i		0		−0.828843	+	0.828843i		0		−0.707107	+	0.707107i		0		−1.29857				0
239.12		0				2.11240i		0		1.47517	−	1.47517i		0		0.707107	−	0.707107i		0		−1.46224				0
239.13		0				2.18785i		0		2.52084	−	2.52084i		0		−0.707107	+	0.707107i		0		−1.78667				0
239.14		0				3.34181i		0		0.187487	−	0.187487i		0		0.707107	−	0.707107i		0		−8.16768				0
463.1		0			−	3.34181i		0		0.187487	+	0.187487i		0		0.707107	+	0.707107i		0		−8.16768				0
463.2		0			−	2.18785i		0		2.52084	+	2.52084i		0		−0.707107	−	0.707107i		0		−1.78667				0
463.3		0			−	2.11240i		0		1.47517	+	1.47517i		0		0.707107	+	0.707107i		0		−1.46224				0
463.4		0			−	2.07330i		0		−0.828843	−	0.828843i		0		−0.707107	−	0.707107i		0		−1.29857				0
463.5		0			−	1.53405i		0		−2.65155	−	2.65155i		0		0.707107	+	0.707107i		0		0.646698				0
463.6		0			−	0.731249i		0		−1.91599	−	1.91599i		0		0.707107	+	0.707107i		0		2.46528				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
13.d	odd	4	1	inner
52.f	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1456.2.v.b	✓	28
4.b	odd	2	1	inner	1456.2.v.b	✓	28
13.d	odd	4	1	inner	1456.2.v.b	✓	28
52.f	even	4	1	inner	1456.2.v.b	✓	28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1456.2.v.b	✓	28	1.a	even	1	1	trivial
1456.2.v.b	✓	28	4.b	odd	2	1	inner
1456.2.v.b	✓	28	13.d	odd	4	1	inner
1456.2.v.b	✓	28	52.f	even	4	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{14} + 28T_{3}^{12} + 296T_{3}^{10} + 1532T_{3}^{8} + 4092T_{3}^{6} + 5336T_{3}^{4} + 2852T_{3}^{2} + 512 \) acting on \(S_{2}^{\mathrm{new}}(1456, [\chi])\).