Newform orbit 1120.2.bs.a

• Label: 1120.2.bs.a
• Level: $1120$
• Weight: $2$
• Character orbit: 1120.bs
• Analytic conductor: $8.943$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $2$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(8.94324502638\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 8 q^{7} - 16 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
31.1		0		−1.71850	+	2.97653i		0		−0.866025	+	0.500000i		0		1.28454	−	2.31300i		0		−4.40648	−	7.63224i		0
31.2		0		−1.49868	+	2.59579i		0		0.866025	−	0.500000i		0		−2.01575	+	1.71369i		0		−2.99210	−	5.18246i		0
31.3		0		−1.20004	+	2.07854i		0		0.866025	−	0.500000i		0		−1.07489	−	2.41756i		0		−1.38021	−	2.39059i		0
31.4		0		−0.920016	+	1.59351i		0		−0.866025	+	0.500000i		0		−0.777217	−	2.52902i		0		−0.192857	−	0.334038i		0
31.5		0		−0.841539	+	1.45759i		0		−0.866025	+	0.500000i		0		−2.11665	+	1.58739i		0		0.0836257	+	0.144844i		0
31.6		0		−0.377679	+	0.654158i		0		−0.866025	+	0.500000i		0		0.429774	+	2.61061i		0		1.21472	+	2.10395i		0
31.7		0		−0.227710	+	0.394405i		0		0.866025	−	0.500000i		0		1.84985	+	1.89158i		0		1.39630	+	2.41846i		0
31.8		0		−0.152904	+	0.264838i		0		0.866025	−	0.500000i		0		−2.62214	+	0.352697i		0		1.45324	+	2.51709i		0
31.9		0		−0.0845359	+	0.146421i		0		0.866025	−	0.500000i		0		1.91682	−	1.82368i		0		1.48571	+	2.57332i		0
31.10		0		0.474489	−	0.821840i		0		−0.866025	+	0.500000i		0		2.02164	+	1.70674i		0		1.04972	+	1.81817i		0
31.11		0		0.836134	−	1.44823i		0		−0.866025	+	0.500000i		0		−2.63995	+	0.175134i		0		0.101761	+	0.176255i		0
31.12		0		0.939393	−	1.62708i		0		0.866025	−	0.500000i		0		−1.87900	+	1.86262i		0		−0.264919	−	0.458853i		0
31.13		0		1.04582	−	1.81141i		0		0.866025	−	0.500000i		0		−0.628123	−	2.57011i		0		−0.687471	−	1.19073i		0
31.14		0		1.11962	−	1.93924i		0		−0.866025	+	0.500000i		0		−2.63782	−	0.204673i		0		−1.00711	−	1.74436i		0
31.15		0		1.17866	−	2.04151i		0		0.866025	−	0.500000i		0		2.45324	+	0.990765i		0		−1.27850	−	2.21443i		0
31.16		0		1.42749	−	2.47248i		0		−0.866025	+	0.500000i		0		2.43568	−	1.03318i		0		−2.57543	−	4.46078i		0
831.1		0		−1.71850	−	2.97653i		0		−0.866025	−	0.500000i		0		1.28454	+	2.31300i		0		−4.40648	+	7.63224i		0
831.2		0		−1.49868	−	2.59579i		0		0.866025	+	0.500000i		0		−2.01575	−	1.71369i		0		−2.99210	+	5.18246i		0
831.3		0		−1.20004	−	2.07854i		0		0.866025	+	0.500000i		0		−1.07489	+	2.41756i		0		−1.38021	+	2.39059i		0
831.4		0		−0.920016	−	1.59351i		0		−0.866025	−	0.500000i		0		−0.777217	+	2.52902i		0		−0.192857	+	0.334038i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
28.f	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1120.2.bs.a	✓	32
4.b	odd	2	1		1120.2.bs.b	yes	32
7.d	odd	6	1		1120.2.bs.b	yes	32
28.f	even	6	1	inner	1120.2.bs.a	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1120.2.bs.a	✓	32	1.a	even	1	1	trivial
1120.2.bs.a	✓	32	28.f	even	6	1	inner
1120.2.bs.b	yes	32	4.b	odd	2	1
1120.2.bs.b	yes	32	7.d	odd	6	1