Newform orbit 1120.2.bw.h

• Label: 1120.2.bw.h
• Level: $1120$
• Weight: $2$
• Character orbit: 1120.bw
• Analytic conductor: $8.943$
• Analytic rank: $0$
• Dimension: $40$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bw (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.94324502638\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(20\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 8 q^{5} + 40 q^{9} - 4 q^{21} + 24 q^{25} + 24 q^{29} - 40 q^{41} - 8 q^{45} - 52 q^{49} - 44 q^{61} + 16 q^{65} - 56 q^{69} - 4 q^{81} - 72 q^{85} - 76 q^{89}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
289.1		0		−2.73849	+	1.58107i		0		2.12487	+	0.696361i		0		−2.30440	−	1.29991i		0		3.49953	−	6.06137i		0
289.2		0		−2.73849	+	1.58107i		0		−1.66550	−	1.49201i		0		−2.30440	−	1.29991i		0		3.49953	−	6.06137i		0
289.3		0		−2.25275	+	1.30063i		0		−1.24022	+	1.86061i		0		2.63098	−	0.279192i		0		1.88326	−	3.26190i		0
289.4		0		−2.25275	+	1.30063i		0		−0.991222	+	2.00437i		0		2.63098	−	0.279192i		0		1.88326	−	3.26190i		0
289.5		0		−2.04145	+	1.17863i		0		−0.800879	−	2.08772i		0		0.745750	+	2.53848i		0		1.27835	−	2.21416i		0
289.6		0		−2.04145	+	1.17863i		0		2.20846	−	0.350280i		0		0.745750	+	2.53848i		0		1.27835	−	2.21416i		0
289.7		0		−1.21235	+	0.699953i		0		−1.99091	−	1.01797i		0		0.374974	−	2.61904i		0		−0.520132	+	0.900895i		0
289.8		0		−1.21235	+	0.699953i		0		1.87704	+	1.21520i		0		0.374974	−	2.61904i		0		−0.520132	+	0.900895i		0
289.9		0		−0.733819	+	0.423671i		0		−2.17978	+	0.498541i		0		−1.14933	+	2.38308i		0		−1.14101	+	1.97628i		0
289.10		0		−0.733819	+	0.423671i		0		0.658143	+	2.13702i		0		−1.14933	+	2.38308i		0		−1.14101	+	1.97628i		0
289.11		0		0.733819	−	0.423671i		0		0.658143	+	2.13702i		0		1.14933	−	2.38308i		0		−1.14101	+	1.97628i		0
289.12		0		0.733819	−	0.423671i		0		−2.17978	+	0.498541i		0		1.14933	−	2.38308i		0		−1.14101	+	1.97628i		0
289.13		0		1.21235	−	0.699953i		0		1.87704	+	1.21520i		0		−0.374974	+	2.61904i		0		−0.520132	+	0.900895i		0
289.14		0		1.21235	−	0.699953i		0		−1.99091	−	1.01797i		0		−0.374974	+	2.61904i		0		−0.520132	+	0.900895i		0
289.15		0		2.04145	−	1.17863i		0		2.20846	−	0.350280i		0		−0.745750	−	2.53848i		0		1.27835	−	2.21416i		0
289.16		0		2.04145	−	1.17863i		0		−0.800879	−	2.08772i		0		−0.745750	−	2.53848i		0		1.27835	−	2.21416i		0
289.17		0		2.25275	−	1.30063i		0		−0.991222	+	2.00437i		0		−2.63098	+	0.279192i		0		1.88326	−	3.26190i		0
289.18		0		2.25275	−	1.30063i		0		−1.24022	+	1.86061i		0		−2.63098	+	0.279192i		0		1.88326	−	3.26190i		0
289.19		0		2.73849	−	1.58107i		0		−1.66550	−	1.49201i		0		2.30440	+	1.29991i		0		3.49953	−	6.06137i		0
289.20		0		2.73849	−	1.58107i		0		2.12487	+	0.696361i		0		2.30440	+	1.29991i		0		3.49953	−	6.06137i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
5.b	even	2	1	inner
7.c	even	3	1	inner
20.d	odd	2	1	inner
28.g	odd	6	1	inner
35.j	even	6	1	inner
140.p	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1120.2.bw.h	✓	40
4.b	odd	2	1	inner	1120.2.bw.h	✓	40
5.b	even	2	1	inner	1120.2.bw.h	✓	40
7.c	even	3	1	inner	1120.2.bw.h	✓	40
20.d	odd	2	1	inner	1120.2.bw.h	✓	40
28.g	odd	6	1	inner	1120.2.bw.h	✓	40
35.j	even	6	1	inner	1120.2.bw.h	✓	40
140.p	odd	6	1	inner	1120.2.bw.h	✓	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1120.2.bw.h	✓	40	1.a	even	1	1	trivial
1120.2.bw.h	✓	40	4.b	odd	2	1	inner
1120.2.bw.h	✓	40	5.b	even	2	1	inner
1120.2.bw.h	✓	40	7.c	even	3	1	inner
1120.2.bw.h	✓	40	20.d	odd	2	1	inner
1120.2.bw.h	✓	40	28.g	odd	6	1	inner
1120.2.bw.h	✓	40	35.j	even	6	1	inner
1120.2.bw.h	✓	40	140.p	odd	6	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1120, [\chi])\):

T3^20 - 25*T3^18 + 403*T3^16 - 3874*T3^14 + 27101*T3^12 - 124915*T3^10 + 415293*T3^8 - 798378*T3^6 + 1076987*T3^4 - 652257*T3^2 + 279841

T11^20 + 66*T11^18 + 2927*T11^16 + 72554*T11^14 + 1308857*T11^12 + 13557888*T11^10 + 96520448*T11^8 + 152625152*T11^6 + 183566336*T11^4 + 61865984*T11^2 + 16777216