Newform orbit 1008.3.o.b

• Label: 1008.3.o.b
• Level: $1008$
• Weight: $3$
• Character orbit: 1008.o
• Analytic conductor: $27.466$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1008.o (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(27.4660106475\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 264 q^{25} - 96 q^{37} - 312 q^{49} - 96 q^{85}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1007.1		0			0			0		−9.41321				0		−3.32249	−	6.16125i		0			0			0
1007.2		0			0			0		−9.41321				0		3.32249	−	6.16125i		0			0			0
1007.3		0			0			0		−9.41321				0		3.32249	+	6.16125i		0			0			0
1007.4		0			0			0		−9.41321				0		−3.32249	+	6.16125i		0			0			0
1007.5		0			0			0		−4.34452				0		−0.646021	−	6.97013i		0			0			0
1007.6		0			0			0		−4.34452				0		0.646021	−	6.97013i		0			0			0
1007.7		0			0			0		−4.34452				0		0.646021	+	6.97013i		0			0			0
1007.8		0			0			0		−4.34452				0		−0.646021	+	6.97013i		0			0			0
1007.9		0			0			0		−0.718749				0		−6.52255	−	2.54092i		0			0			0
1007.10		0			0			0		−0.718749				0		6.52255	+	2.54092i		0			0			0
1007.11		0			0			0		−0.718749				0		6.52255	−	2.54092i		0			0			0
1007.12		0			0			0		−0.718749				0		−6.52255	+	2.54092i		0			0			0
1007.13		0			0			0		0.718749				0		−6.52255	−	2.54092i		0			0			0
1007.14		0			0			0		0.718749				0		6.52255	+	2.54092i		0			0			0
1007.15		0			0			0		0.718749				0		6.52255	−	2.54092i		0			0			0
1007.16		0			0			0		0.718749				0		−6.52255	+	2.54092i		0			0			0
1007.17		0			0			0		4.34452				0		−0.646021	−	6.97013i		0			0			0
1007.18		0			0			0		4.34452				0		0.646021	−	6.97013i		0			0			0
1007.19		0			0			0		4.34452				0		0.646021	+	6.97013i		0			0			0
1007.20		0			0			0		4.34452				0		−0.646021	+	6.97013i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
4.b	odd	2	1	inner
7.b	odd	2	1	inner
12.b	even	2	1	inner
21.c	even	2	1	inner
28.d	even	2	1	inner
84.h	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1008.3.o.b	✓	24
3.b	odd	2	1	inner	1008.3.o.b	✓	24
4.b	odd	2	1	inner	1008.3.o.b	✓	24
7.b	odd	2	1	inner	1008.3.o.b	✓	24
12.b	even	2	1	inner	1008.3.o.b	✓	24
21.c	even	2	1	inner	1008.3.o.b	✓	24
28.d	even	2	1	inner	1008.3.o.b	✓	24
84.h	odd	2	1	inner	1008.3.o.b	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1008.3.o.b	✓	24	1.a	even	1	1	trivial
1008.3.o.b	✓	24	3.b	odd	2	1	inner
1008.3.o.b	✓	24	4.b	odd	2	1	inner
1008.3.o.b	✓	24	7.b	odd	2	1	inner
1008.3.o.b	✓	24	12.b	even	2	1	inner
1008.3.o.b	✓	24	21.c	even	2	1	inner
1008.3.o.b	✓	24	28.d	even	2	1	inner
1008.3.o.b	✓	24	84.h	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{6} - 108T_{5}^{4} + 1728T_{5}^{2} - 864 \) acting on \(S_{3}^{\mathrm{new}}(1008, [\chi])\).