Newform orbit 1440.2.bw.b

• Label: 1440.2.bw.b
• Level: $1440$
• Weight: $2$
• Character orbit: 1440.bw
• Analytic conductor: $11.498$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.bw (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.4984578911\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(24\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
191.1		0		−1.73193	−	0.0205952i		0		0.866025	−	0.500000i		0		−0.491447	−	0.283737i		0		2.99915	+	0.0713388i		0
191.2		0		−1.66461	−	0.478600i		0		−0.866025	+	0.500000i		0		−3.08353	−	1.78028i		0		2.54188	+	1.59337i		0
191.3		0		−1.60910	−	0.640940i		0		−0.866025	+	0.500000i		0		3.27113	+	1.88859i		0		2.17839	+	2.06267i		0
191.4		0		−1.52522	−	0.820793i		0		−0.866025	+	0.500000i		0		2.21138	+	1.27674i		0		1.65260	+	2.50378i		0
191.5		0		−1.32482	+	1.11573i		0		−0.866025	+	0.500000i		0		−1.43541	−	0.828737i		0		0.510297	−	2.95628i		0
191.6		0		−1.30422	−	1.13974i		0		0.866025	−	0.500000i		0		1.29686	+	0.748740i		0		0.401980	+	2.97295i		0
191.7		0		−1.25980	+	1.18866i		0		0.866025	−	0.500000i		0		−1.30635	−	0.754221i		0		0.174171	−	2.99494i		0
191.8		0		−0.946901	+	1.45030i		0		−0.866025	+	0.500000i		0		−0.356041	−	0.205560i		0		−1.20676	−	2.74659i		0
191.9		0		−0.845351	−	1.51175i		0		0.866025	−	0.500000i		0		−2.58247	−	1.49099i		0		−1.57076	+	2.55592i		0
191.10		0		−0.559432	+	1.63922i		0		0.866025	−	0.500000i		0		2.85834	+	1.65026i		0		−2.37407	−	1.83406i		0
191.11		0		−0.523763	−	1.65096i		0		−0.866025	+	0.500000i		0		0.436082	+	0.251772i		0		−2.45134	+	1.72942i		0
191.12		0		−0.233007	−	1.71631i		0		−0.866025	+	0.500000i		0		−0.912675	−	0.526933i		0		−2.89142	+	0.799824i		0
191.13		0		0.183565	+	1.72230i		0		0.866025	−	0.500000i		0		−1.95329	−	1.12773i		0		−2.93261	+	0.632306i		0
191.14		0		0.312514	−	1.70362i		0		0.866025	−	0.500000i		0		3.32749	+	1.92113i		0		−2.80467	−	1.06481i		0
191.15		0		0.368780	+	1.69234i		0		−0.866025	+	0.500000i		0		−0.730361	−	0.421674i		0		−2.72800	+	1.24820i		0
191.16		0		0.793361	+	1.53967i		0		0.866025	−	0.500000i		0		−2.37166	−	1.36928i		0		−1.74116	+	2.44302i		0
191.17		0		0.933343	+	1.45907i		0		−0.866025	+	0.500000i		0		4.20525	+	2.42790i		0		−1.25774	+	2.72362i		0
191.18		0		1.30441	−	1.13953i		0		0.866025	−	0.500000i		0		−2.83377	−	1.63608i		0		0.402957	−	2.97281i		0
191.19		0		1.42951	+	0.978016i		0		0.866025	−	0.500000i		0		2.45062	+	1.41486i		0		1.08697	+	2.79616i		0
191.20		0		1.46481	−	0.924293i		0		−0.866025	+	0.500000i		0		−4.20282	−	2.42650i		0		1.29137	−	2.70784i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
36.h	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1440.2.bw.b	yes	48
3.b	odd	2	1		4320.2.bw.b		48
4.b	odd	2	1		1440.2.bw.a	✓	48
9.c	even	3	1		4320.2.bw.a		48
9.d	odd	6	1		1440.2.bw.a	✓	48
12.b	even	2	1		4320.2.bw.a		48
36.f	odd	6	1		4320.2.bw.b		48
36.h	even	6	1	inner	1440.2.bw.b	yes	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1440.2.bw.a	✓	48	4.b	odd	2	1
1440.2.bw.a	✓	48	9.d	odd	6	1
1440.2.bw.b	yes	48	1.a	even	1	1	trivial
1440.2.bw.b	yes	48	36.h	even	6	1	inner
4320.2.bw.a		48	9.c	even	3	1
4320.2.bw.a		48	12.b	even	2	1
4320.2.bw.b		48	3.b	odd	2	1
4320.2.bw.b		48	36.f	odd	6	1