Newform orbit 912.2.d.b

• Label: 912.2.d.b
• Level: $912$
• Weight: $2$
• Character orbit: 912.d
• Analytic conductor: $7.282$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.28235666434\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
191.1		0		−1.72850	−	0.110841i		0				3.67549i		0				4.87247i		0		2.97543	+	0.383177i		0
191.2		0		−1.72850	+	0.110841i		0			−	3.67549i		0			−	4.87247i		0		2.97543	−	0.383177i		0
191.3		0		−1.57777	−	0.714595i		0			−	1.85004i		0			−	0.707624i		0		1.97871	+	2.25493i		0
191.4		0		−1.57777	+	0.714595i		0				1.85004i		0				0.707624i		0		1.97871	−	2.25493i		0
191.5		0		−1.50956	−	0.849252i		0				0.771899i		0			−	1.48496i		0		1.55754	+	2.56399i		0
191.6		0		−1.50956	+	0.849252i		0			−	0.771899i		0				1.48496i		0		1.55754	−	2.56399i		0
191.7		0		−0.909651	−	1.47395i		0				2.62895i		0			−	3.58561i		0		−1.34507	+	2.68156i		0
191.8		0		−0.909651	+	1.47395i		0			−	2.62895i		0				3.58561i		0		−1.34507	−	2.68156i		0
191.9		0		−0.881895	−	1.49073i		0				1.27921i		0			−	0.100648i		0		−1.44452	+	2.62933i		0
191.10		0		−0.881895	+	1.49073i		0			−	1.27921i		0				0.100648i		0		−1.44452	−	2.62933i		0
191.11		0		−0.372770	−	1.69146i		0			−	4.46369i		0				2.16484i		0		−2.72208	+	1.26105i		0
191.12		0		−0.372770	+	1.69146i		0				4.46369i		0			−	2.16484i		0		−2.72208	−	1.26105i		0
191.13		0		0.372770	−	1.69146i		0				4.46369i		0				2.16484i		0		−2.72208	−	1.26105i		0
191.14		0		0.372770	+	1.69146i		0			−	4.46369i		0			−	2.16484i		0		−2.72208	+	1.26105i		0
191.15		0		0.881895	−	1.49073i		0			−	1.27921i		0			−	0.100648i		0		−1.44452	−	2.62933i		0
191.16		0		0.881895	+	1.49073i		0				1.27921i		0				0.100648i		0		−1.44452	+	2.62933i		0
191.17		0		0.909651	−	1.47395i		0			−	2.62895i		0			−	3.58561i		0		−1.34507	−	2.68156i		0
191.18		0		0.909651	+	1.47395i		0				2.62895i		0				3.58561i		0		−1.34507	+	2.68156i		0
191.19		0		1.50956	−	0.849252i		0			−	0.771899i		0			−	1.48496i		0		1.55754	−	2.56399i		0
191.20		0		1.50956	+	0.849252i		0				0.771899i		0				1.48496i		0		1.55754	+	2.56399i		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
12.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	912.2.d.b	✓	24
3.b	odd	2	1	inner	912.2.d.b	✓	24
4.b	odd	2	1	inner	912.2.d.b	✓	24
12.b	even	2	1	inner	912.2.d.b	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
912.2.d.b	✓	24	1.a	even	1	1	trivial
912.2.d.b	✓	24	3.b	odd	2	1	inner
912.2.d.b	✓	24	4.b	odd	2	1	inner
912.2.d.b	✓	24	12.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{12} + 46T_{5}^{10} + 737T_{5}^{8} + 5040T_{5}^{6} + 14964T_{5}^{4} + 17696T_{5}^{2} + 6208 \) acting on \(S_{2}^{\mathrm{new}}(912, [\chi])\).