Newform orbit 2016.3.g.c

• Label: 2016.3.g.c
• Level: $2016$
• Weight: $3$
• Character orbit: 2016.g
• Analytic conductor: $54.932$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2016.g (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(54.9320212950\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	no (minimal twist has level 504)
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.

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1135.1		0			0			0			−	1.24577i		0			−	2.64575i		0			0			0
1135.2		0			0			0				1.24577i		0				2.64575i		0			0			0
1135.3		0			0			0			−	9.01528i		0				2.64575i		0			0			0
1135.4		0			0			0				9.01528i		0			−	2.64575i		0			0			0
1135.5		0			0			0			−	6.98187i		0				2.64575i		0			0			0
1135.6		0			0			0				6.98187i		0			−	2.64575i		0			0			0
1135.7		0			0			0			−	6.98819i		0				2.64575i		0			0			0
1135.8		0			0			0				6.98819i		0			−	2.64575i		0			0			0
1135.9		0			0			0			−	2.67381i		0			−	2.64575i		0			0			0
1135.10		0			0			0				2.67381i		0				2.64575i		0			0			0
1135.11		0			0			0			−	2.10762i		0				2.64575i		0			0			0
1135.12		0			0			0				2.10762i		0			−	2.64575i		0			0			0
1135.13		0			0			0			−	2.10762i		0			−	2.64575i		0			0			0
1135.14		0			0			0				2.10762i		0				2.64575i		0			0			0
1135.15		0			0			0			−	2.67381i		0				2.64575i		0			0			0
1135.16		0			0			0				2.67381i		0			−	2.64575i		0			0			0
1135.17		0			0			0			−	6.98819i		0			−	2.64575i		0			0			0
1135.18		0			0			0				6.98819i		0				2.64575i		0			0			0
1135.19		0			0			0			−	6.98187i		0			−	2.64575i		0			0			0
1135.20		0			0			0				6.98187i		0				2.64575i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
8.d	odd	2	1	inner
24.f	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2016.3.g.c		24
3.b	odd	2	1	inner	2016.3.g.c		24
4.b	odd	2	1		504.3.g.c	✓	24
8.b	even	2	1		504.3.g.c	✓	24
8.d	odd	2	1	inner	2016.3.g.c		24
12.b	even	2	1		504.3.g.c	✓	24
24.f	even	2	1	inner	2016.3.g.c		24
24.h	odd	2	1		504.3.g.c	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
504.3.g.c	✓	24	4.b	odd	2	1
504.3.g.c	✓	24	8.b	even	2	1
504.3.g.c	✓	24	12.b	even	2	1
504.3.g.c	✓	24	24.h	odd	2	1
2016.3.g.c		24	1.a	even	1	1	trivial
2016.3.g.c		24	3.b	odd	2	1	inner
2016.3.g.c		24	8.d	odd	2	1	inner
2016.3.g.c		24	24.f	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{12} + 192T_{5}^{10} + 12712T_{5}^{8} + 337952T_{5}^{6} + 3064720T_{5}^{4} + 10133120T_{5}^{2} + 9535744 \) acting on \(S_{3}^{\mathrm{new}}(2016, [\chi])\).