Newform orbit 1440.4.k.e

• Label: 1440.4.k.e
• Level: $1440$
• Weight: $4$
• Character orbit: 1440.k
• Analytic conductor: $84.963$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1440.k (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(84.9627504083\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	no (minimal twist has level 360)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 56 q^{7} - 600 q^{25} - 264 q^{31} + 456 q^{49} - 880 q^{55} - 432 q^{73} + 1656 q^{79} + 1584 q^{97}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
721.1		0			0			0			−	5.00000i		0		17.4426				0			0			0
721.2		0			0			0				5.00000i		0		17.4426				0			0			0
721.3		0			0			0			−	5.00000i		0		−31.9487				0			0			0
721.4		0			0			0				5.00000i		0		−31.9487				0			0			0
721.5		0			0			0			−	5.00000i		0		16.6486				0			0			0
721.6		0			0			0				5.00000i		0		16.6486				0			0			0
721.7		0			0			0			−	5.00000i		0		−20.1838				0			0			0
721.8		0			0			0				5.00000i		0		−20.1838				0			0			0
721.9		0			0			0			−	5.00000i		0		−6.76306				0			0			0
721.10		0			0			0				5.00000i		0		−6.76306				0			0			0
721.11		0			0			0			−	5.00000i		0		17.4426				0			0			0
721.12		0			0			0				5.00000i		0		17.4426				0			0			0
721.13		0			0			0			−	5.00000i		0		−20.1838				0			0			0
721.14		0			0			0				5.00000i		0		−20.1838				0			0			0
721.15		0			0			0			−	5.00000i		0		10.8044				0			0			0
721.16		0			0			0				5.00000i		0		10.8044				0			0			0
721.17		0			0			0			−	5.00000i		0		−31.9487				0			0			0
721.18		0			0			0				5.00000i		0		−31.9487				0			0			0
721.19		0			0			0			−	5.00000i		0		16.6486				0			0			0
721.20		0			0			0				5.00000i		0		16.6486				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	1440.4.k.e		24
3.b	odd	2	1	inner	1440.4.k.e		24
4.b	odd	2	1		360.4.k.e	✓	24
8.b	even	2	1	inner	1440.4.k.e		24
8.d	odd	2	1		360.4.k.e	✓	24
12.b	even	2	1		360.4.k.e	✓	24
24.f	even	2	1		360.4.k.e	✓	24
24.h	odd	2	1	inner	1440.4.k.e		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
360.4.k.e	✓	24	4.b	odd	2	1
360.4.k.e	✓	24	8.d	odd	2	1
360.4.k.e	✓	24	12.b	even	2	1
360.4.k.e	✓	24	24.f	even	2	1
1440.4.k.e		24	1.a	even	1	1	trivial
1440.4.k.e		24	3.b	odd	2	1	inner
1440.4.k.e		24	8.b	even	2	1	inner
1440.4.k.e		24	24.h	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{6} + 14T_{7}^{5} - 988T_{7}^{4} - 4760T_{7}^{3} + 276448T_{7}^{2} - 256640T_{7} - 13683200 \) acting on \(S_{4}^{\mathrm{new}}(1440, [\chi])\).