Newform orbit 440.2.v.b

• Label: 440.2.v.b
• Level: $440$
• Weight: $2$
• Character orbit: 440.v
• Analytic conductor: $3.513$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.v (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.51341768894\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 32 * q - 4 * q^3 + 8 * q^5 - 8 * q^11 + 24 * q^15 - 28 * q^23 + 4 * q^25 - 4 * q^27 + 24 * q^31 - 12 * q^33 + 4 * q^37 - 28 * q^45 + 8 * q^47 + 24 * q^53 + 12 * q^55 - 52 * q^67 + 48 * q^71 - 24 * q^75 + 56 * q^77 - 24 * q^81 - 16 * q^91 - 76 * q^93 - 36 * q^97

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
153.1		0		−2.10267	−	2.10267i		0		−2.17481	+	0.519798i		0		−3.44647	−	3.44647i		0				5.84244i		0
153.2		0		−2.10267	−	2.10267i		0		−2.17481	+	0.519798i		0		3.44647	+	3.44647i		0				5.84244i		0
153.3		0		−1.62830	−	1.62830i		0		1.07475	+	1.96085i		0		−1.24708	−	1.24708i		0				2.30275i		0
153.4		0		−1.62830	−	1.62830i		0		1.07475	+	1.96085i		0		1.24708	+	1.24708i		0				2.30275i		0
153.5		0		−1.50516	−	1.50516i		0		1.52592	−	1.63449i		0		−1.92066	−	1.92066i		0				1.53101i		0
153.6		0		−1.50516	−	1.50516i		0		1.52592	−	1.63449i		0		1.92066	+	1.92066i		0				1.53101i		0
153.7		0		−0.185627	−	0.185627i		0		−2.05027	+	0.892416i		0		−0.202657	−	0.202657i		0			−	2.93108i		0
153.8		0		−0.185627	−	0.185627i		0		−2.05027	+	0.892416i		0		0.202657	+	0.202657i		0			−	2.93108i		0
153.9		0		0.179637	+	0.179637i		0		2.16046	+	0.576544i		0		−1.58807	−	1.58807i		0			−	2.93546i		0
153.10		0		0.179637	+	0.179637i		0		2.16046	+	0.576544i		0		1.58807	+	1.58807i		0			−	2.93546i		0
153.11		0		0.395428	+	0.395428i		0		−0.0577165	−	2.23532i		0		−2.57694	−	2.57694i		0			−	2.68727i		0
153.12		0		0.395428	+	0.395428i		0		−0.0577165	−	2.23532i		0		2.57694	+	2.57694i		0			−	2.68727i		0
153.13		0		1.78145	+	1.78145i		0		−0.300869	+	2.21573i		0		−1.52953	−	1.52953i		0				3.34712i		0
153.14		0		1.78145	+	1.78145i		0		−0.300869	+	2.21573i		0		1.52953	+	1.52953i		0				3.34712i		0
153.15		0		2.06525	+	2.06525i		0		1.82253	−	1.29552i		0		−1.52796	−	1.52796i		0				5.53050i		0
153.16		0		2.06525	+	2.06525i		0		1.82253	−	1.29552i		0		1.52796	+	1.52796i		0				5.53050i		0
417.1		0		−2.10267	+	2.10267i		0		−2.17481	−	0.519798i		0		−3.44647	+	3.44647i		0			−	5.84244i		0
417.2		0		−2.10267	+	2.10267i		0		−2.17481	−	0.519798i		0		3.44647	−	3.44647i		0			−	5.84244i		0
417.3		0		−1.62830	+	1.62830i		0		1.07475	−	1.96085i		0		−1.24708	+	1.24708i		0			−	2.30275i		0
417.4		0		−1.62830	+	1.62830i		0		1.07475	−	1.96085i		0		1.24708	−	1.24708i		0			−	2.30275i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
11.b	odd	2	1	inner
55.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	440.2.v.b	✓	32
4.b	odd	2	1		880.2.bd.i		32
5.c	odd	4	1	inner	440.2.v.b	✓	32
11.b	odd	2	1	inner	440.2.v.b	✓	32
20.e	even	4	1		880.2.bd.i		32
44.c	even	2	1		880.2.bd.i		32
55.e	even	4	1	inner	440.2.v.b	✓	32
220.i	odd	4	1		880.2.bd.i		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
440.2.v.b	✓	32	1.a	even	1	1	trivial
440.2.v.b	✓	32	5.c	odd	4	1	inner
440.2.v.b	✓	32	11.b	odd	2	1	inner
440.2.v.b	✓	32	55.e	even	4	1	inner
880.2.bd.i		32	4.b	odd	2	1
880.2.bd.i		32	20.e	even	4	1
880.2.bd.i		32	44.c	even	2	1
880.2.bd.i		32	220.i	odd	4	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^16 + 2*T3^15 + 2*T3^14 - 2*T3^13 + 114*T3^12 + 226*T3^11 + 226*T3^10 - 218*T3^9 + 3001*T3^8 + 5912*T3^7 + 6032*T3^6 - 6480*T3^5 + 3528*T3^4 + 64*T3^3 + 32*T3^2 - 32*T3 + 16