Newform orbit 2448.2.e.b

• Label: 2448.2.e.b
• Level: $2448$
• Weight: $2$
• Character orbit: 2448.e
• Analytic conductor: $19.547$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2448.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(19.5473784148\)
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.

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1871.1		0			0			0			−	3.60691i		0			−	3.68009i		0			0			0
1871.2		0			0			0			−	3.60691i		0				3.68009i		0			0			0
1871.3		0			0			0			−	3.43389i		0			−	1.08828i		0			0			0
1871.4		0			0			0			−	3.43389i		0				1.08828i		0			0			0
1871.5		0			0			0			−	2.30101i		0			−	3.37073i		0			0			0
1871.6		0			0			0			−	2.30101i		0				3.37073i		0			0			0
1871.7		0			0			0			−	1.73995i		0			−	0.271290i		0			0			0
1871.8		0			0			0			−	1.73995i		0				0.271290i		0			0			0
1871.9		0			0			0			−	0.826971i		0			−	5.04130i		0			0			0
1871.10		0			0			0			−	0.826971i		0				5.04130i		0			0			0
1871.11		0			0			0			−	0.438941i		0			−	0.649951i		0			0			0
1871.12		0			0			0			−	0.438941i		0				0.649951i		0			0			0
1871.13		0			0			0				0.438941i		0			−	0.649951i		0			0			0
1871.14		0			0			0				0.438941i		0				0.649951i		0			0			0
1871.15		0			0			0				0.826971i		0			−	5.04130i		0			0			0
1871.16		0			0			0				0.826971i		0				5.04130i		0			0			0
1871.17		0			0			0				1.73995i		0			−	0.271290i		0			0			0
1871.18		0			0			0				1.73995i		0				0.271290i		0			0			0
1871.19		0			0			0				2.30101i		0			−	3.37073i		0			0			0
1871.20		0			0			0				2.30101i		0				3.37073i		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
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	2448.2.e.b	✓	24
3.b	odd	2	1	inner	2448.2.e.b	✓	24
4.b	odd	2	1	inner	2448.2.e.b	✓	24
12.b	even	2	1	inner	2448.2.e.b	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2448.2.e.b	✓	24	1.a	even	1	1	trivial
2448.2.e.b	✓	24	3.b	odd	2	1	inner
2448.2.e.b	✓	24	4.b	odd	2	1	inner
2448.2.e.b	✓	24	12.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{12} + 34T_{5}^{10} + 405T_{5}^{8} + 2008T_{5}^{6} + 3976T_{5}^{4} + 2376T_{5}^{2} + 324 \) acting on \(S_{2}^{\mathrm{new}}(2448, [\chi])\).