Newform orbit 112.10.f.b

• Label: 112.10.f.b
• Level: $112$
• Weight: $10$
• Character orbit: 112.f
• Analytic conductor: $57.684$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	112.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(57.6840136504\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 155768 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
111.1		0		−270.294				0			−	701.713i		0		2728.89	−	5736.44i		0		53376.0				0
111.2		0		−270.294				0				701.713i		0		2728.89	+	5736.44i		0		53376.0				0
111.3		0		−170.771				0			−	701.626i		0		911.052	−	6286.78i		0		9479.76				0
111.4		0		−170.771				0				701.626i		0		911.052	+	6286.78i		0		9479.76				0
111.5		0		−168.927				0				1693.73i		0		−6136.85	−	1640.94i		0		8853.27				0
111.6		0		−168.927				0			−	1693.73i		0		−6136.85	+	1640.94i		0		8853.27				0
111.7		0		−139.194				0			−	2541.34i		0		−1354.15	+	6206.44i		0		−308.104				0
111.8		0		−139.194				0				2541.34i		0		−1354.15	−	6206.44i		0		−308.104				0
111.9		0		−64.1982				0				287.809i		0		6348.43	−	225.841i		0		−15561.6				0
111.10		0		−64.1982				0			−	287.809i		0		6348.43	+	225.841i		0		−15561.6				0
111.11		0		−52.7793				0			−	1902.89i		0		−2477.17	−	5849.55i		0		−16897.3				0
111.12		0		−52.7793				0				1902.89i		0		−2477.17	+	5849.55i		0		−16897.3				0
111.13		0		52.7793				0			−	1902.89i		0		2477.17	+	5849.55i		0		−16897.3				0
111.14		0		52.7793				0				1902.89i		0		2477.17	−	5849.55i		0		−16897.3				0
111.15		0		64.1982				0				287.809i		0		−6348.43	+	225.841i		0		−15561.6				0
111.16		0		64.1982				0			−	287.809i		0		−6348.43	−	225.841i		0		−15561.6				0
111.17		0		139.194				0			−	2541.34i		0		1354.15	−	6206.44i		0		−308.104				0
111.18		0		139.194				0				2541.34i		0		1354.15	+	6206.44i		0		−308.104				0
111.19		0		168.927				0				1693.73i		0		6136.85	+	1640.94i		0		8853.27				0
111.20		0		168.927				0			−	1693.73i		0		6136.85	−	1640.94i		0		8853.27				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
7.b	odd	2	1	inner
28.d	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	112.10.f.b	✓	24
4.b	odd	2	1	inner	112.10.f.b	✓	24
7.b	odd	2	1	inner	112.10.f.b	✓	24
28.d	even	2	1	inner	112.10.f.b	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
112.10.f.b	✓	24	1.a	even	1	1	trivial
112.10.f.b	✓	24	4.b	odd	2	1	inner
112.10.f.b	✓	24	7.b	odd	2	1	inner
112.10.f.b	✓	24	28.d	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^12 - 157040*T3^10 + 8629513072*T3^8 - 212683279947264*T3^6 + 2360458863124289280*T3^4 - 9957237037762047750144*T3^2 + 13524241993722692755329024