Newform orbit 3744.2.g.f

• Label: 3744.2.g.f
• Level: $3744$
• Weight: $2$
• Character orbit: 3744.g
• Analytic conductor: $29.896$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3744.g (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(29.8959905168\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	no (minimal twist has level 936)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{7} - 24 q^{25} - 40 q^{31} + 24 q^{49} + 16 q^{55} - 16 q^{97}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1873.1		0			0			0			−	1.61588i		0		1.38556				0			0			0
1873.2		0			0			0				1.61588i		0		1.38556				0			0			0
1873.3		0			0			0			−	2.32782i		0		4.85152				0			0			0
1873.4		0			0			0				2.32782i		0		4.85152				0			0			0
1873.5		0			0			0			−	0.839709i		0		0.482293				0			0			0
1873.6		0			0			0				0.839709i		0		0.482293				0			0			0
1873.7		0			0			0			−	2.32782i		0		4.85152				0			0			0
1873.8		0			0			0				2.32782i		0		4.85152				0			0			0
1873.9		0			0			0			−	3.06504i		0		1.53955				0			0			0
1873.10		0			0			0				3.06504i		0		1.53955				0			0			0
1873.11		0			0			0			−	4.18566i		0		−2.70923				0			0			0
1873.12		0			0			0				4.18566i		0		−2.70923				0			0			0
1873.13		0			0			0			−	3.06504i		0		1.53955				0			0			0
1873.14		0			0			0				3.06504i		0		1.53955				0			0			0
1873.15		0			0			0			−	0.592273i		0		−3.54968				0			0			0
1873.16		0			0			0				0.592273i		0		−3.54968				0			0			0
1873.17		0			0			0			−	0.592273i		0		−3.54968				0			0			0
1873.18		0			0			0				0.592273i		0		−3.54968				0			0			0
1873.19		0			0			0			−	0.839709i		0		0.482293				0			0			0
1873.20		0			0			0				0.839709i		0		0.482293				0			0			0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3744.2.g.f		24
3.b	odd	2	1	inner	3744.2.g.f		24
4.b	odd	2	1		936.2.g.f	✓	24
8.b	even	2	1	inner	3744.2.g.f		24
8.d	odd	2	1		936.2.g.f	✓	24
12.b	even	2	1		936.2.g.f	✓	24
24.f	even	2	1		936.2.g.f	✓	24
24.h	odd	2	1	inner	3744.2.g.f		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
936.2.g.f	✓	24	4.b	odd	2	1
936.2.g.f	✓	24	8.d	odd	2	1
936.2.g.f	✓	24	12.b	even	2	1
936.2.g.f	✓	24	24.f	even	2	1
3744.2.g.f		24	1.a	even	1	1	trivial
3744.2.g.f		24	3.b	odd	2	1	inner
3744.2.g.f		24	8.b	even	2	1	inner
3744.2.g.f		24	24.h	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{12} + 36T_{5}^{10} + 432T_{5}^{8} + 2128T_{5}^{6} + 4224T_{5}^{4} + 2880T_{5}^{2} + 576 \) acting on \(S_{2}^{\mathrm{new}}(3744, [\chi])\).