Newform orbit 1008.2.bh.e

• Label: 1008.2.bh.e
• Level: $1008$
• Weight: $2$
• Character orbit: 1008.bh
• Analytic conductor: $8.049$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.bh (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.04892052375\)
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 algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 32 * q - 4 * q^9 + 2 * q^13 - 18 * q^17 + 8 * q^21 - 32 * q^25 + 12 * q^29 + 22 * q^33 - 2 * q^37 + 22 * q^45 + 2 * q^49 + 24 * q^53 - 10 * q^57 - 14 * q^61 - 78 * q^65 - 62 * q^69 - 28 * q^73 + 6 * q^77 + 16 * q^81 + 12 * q^85 - 42 * q^89 + 66 * q^93 + 2 * q^97

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
95.1		0		−1.72081	+	0.197001i		0				3.83221i		0		−1.47304	+	2.19776i		0		2.92238	−	0.678002i		0
95.2		0		−1.67617	−	0.436425i		0			−	3.09416i		0		−2.62391	+	0.339265i		0		2.61907	+	1.46304i		0
95.3		0		−1.44046	+	0.961802i		0				0.0197813i		0		−1.39197	−	2.24998i		0		1.14988	−	2.77088i		0
95.4		0		−1.27304	−	1.17446i		0				1.36474i		0		1.50769	−	2.17414i		0		0.241269	+	2.99028i		0
95.5		0		−1.22805	+	1.22143i		0				1.99113i		0		2.41342	+	1.08417i		0		0.0161982	−	2.99996i		0
95.6		0		−0.533625	+	1.64780i		0			−	3.47777i		0		−0.209560	+	2.63744i		0		−2.43049	−	1.75861i		0
95.7		0		−0.473647	−	1.66603i		0			−	1.99364i		0		1.57802	+	2.12364i		0		−2.55132	+	1.57822i		0
95.8		0		−0.128485	−	1.72728i		0				1.35771i		0		−2.57408	+	0.611637i		0		−2.96698	+	0.443860i		0
95.9		0		0.128485	+	1.72728i		0				1.35771i		0		2.57408	−	0.611637i		0		−2.96698	+	0.443860i		0
95.10		0		0.473647	+	1.66603i		0			−	1.99364i		0		−1.57802	−	2.12364i		0		−2.55132	+	1.57822i		0
95.11		0		0.533625	−	1.64780i		0			−	3.47777i		0		0.209560	−	2.63744i		0		−2.43049	−	1.75861i		0
95.12		0		1.22805	−	1.22143i		0				1.99113i		0		−2.41342	−	1.08417i		0		0.0161982	−	2.99996i		0
95.13		0		1.27304	+	1.17446i		0				1.36474i		0		−1.50769	+	2.17414i		0		0.241269	+	2.99028i		0
95.14		0		1.44046	−	0.961802i		0				0.0197813i		0		1.39197	+	2.24998i		0		1.14988	−	2.77088i		0
95.15		0		1.67617	+	0.436425i		0			−	3.09416i		0		2.62391	−	0.339265i		0		2.61907	+	1.46304i		0
95.16		0		1.72081	−	0.197001i		0				3.83221i		0		1.47304	−	2.19776i		0		2.92238	−	0.678002i		0
191.1		0		−1.72081	−	0.197001i		0			−	3.83221i		0		−1.47304	−	2.19776i		0		2.92238	+	0.678002i		0
191.2		0		−1.67617	+	0.436425i		0				3.09416i		0		−2.62391	−	0.339265i		0		2.61907	−	1.46304i		0
191.3		0		−1.44046	−	0.961802i		0			−	0.0197813i		0		−1.39197	+	2.24998i		0		1.14988	+	2.77088i		0
191.4		0		−1.27304	+	1.17446i		0			−	1.36474i		0		1.50769	+	2.17414i		0		0.241269	−	2.99028i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
63.n	odd	6	1	inner
252.o	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1008.2.bh.e	✓	32
3.b	odd	2	1		3024.2.bh.e		32
4.b	odd	2	1	inner	1008.2.bh.e	✓	32
7.c	even	3	1		1008.2.cj.e	yes	32
9.c	even	3	1		3024.2.cj.e		32
9.d	odd	6	1		1008.2.cj.e	yes	32
12.b	even	2	1		3024.2.bh.e		32
21.h	odd	6	1		3024.2.cj.e		32
28.g	odd	6	1		1008.2.cj.e	yes	32
36.f	odd	6	1		3024.2.cj.e		32
36.h	even	6	1		1008.2.cj.e	yes	32
63.g	even	3	1		3024.2.bh.e		32
63.n	odd	6	1	inner	1008.2.bh.e	✓	32
84.n	even	6	1		3024.2.cj.e		32
252.o	even	6	1	inner	1008.2.bh.e	✓	32
252.bl	odd	6	1		3024.2.bh.e		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1008.2.bh.e	✓	32	1.a	even	1	1	trivial
1008.2.bh.e	✓	32	4.b	odd	2	1	inner
1008.2.bh.e	✓	32	63.n	odd	6	1	inner
1008.2.bh.e	✓	32	252.o	even	6	1	inner
1008.2.cj.e	yes	32	7.c	even	3	1
1008.2.cj.e	yes	32	9.d	odd	6	1
1008.2.cj.e	yes	32	28.g	odd	6	1
1008.2.cj.e	yes	32	36.h	even	6	1
3024.2.bh.e		32	3.b	odd	2	1
3024.2.bh.e		32	12.b	even	2	1
3024.2.bh.e		32	63.g	even	3	1
3024.2.bh.e		32	252.bl	odd	6	1
3024.2.cj.e		32	9.c	even	3	1
3024.2.cj.e		32	21.h	odd	6	1
3024.2.cj.e		32	36.f	odd	6	1
3024.2.cj.e		32	84.n	even	6	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1008, [\chi])\):

\( T_{5}^{16} + 48T_{5}^{14} + 906T_{5}^{12} + 8608T_{5}^{10} + 44073T_{5}^{8} + 121827T_{5}^{6} + 169186T_{5}^{4} + 92067T_{5}^{2} + 36 \)

T11^16 - 102*T11^14 + 3879*T11^12 - 68443*T11^10 + 580932*T11^8 - 2476578*T11^6 + 5234152*T11^4 - 4955499*T11^2 + 1679616