Newform orbit 1024.4.b.m

• Label: 1024.4.b.m
• Level: $1024$
• Weight: $4$
• Character orbit: 1024.b
• Analytic conductor: $60.418$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1024 = 2^{10} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1024.b (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(60.4179558459\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	no (minimal twist has level 512)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 216 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
513.1		0			−	9.32315i		0			−	1.51080i		0		−26.3526				0		−59.9211				0
513.2		0			−	9.32315i		0				1.51080i		0		26.3526				0		−59.9211				0
513.3		0			−	7.23522i		0			−	2.33804i		0		5.40314				0		−25.3484				0
513.4		0			−	7.23522i		0				2.33804i		0		−5.40314				0		−25.3484				0
513.5		0			−	6.38533i		0			−	18.9781i		0		−26.2604				0		−13.7725				0
513.6		0			−	6.38533i		0				18.9781i		0		26.2604				0		−13.7725				0
513.7		0			−	4.95293i		0			−	18.5500i		0		19.2842				0		2.46849				0
513.8		0			−	4.95293i		0				18.5500i		0		−19.2842				0		2.46849				0
513.9		0			−	3.36468i		0			−	12.3022i		0		15.0403				0		15.6789				0
513.10		0			−	3.36468i		0				12.3022i		0		−15.0403				0		15.6789				0
513.11		0			−	0.324689i		0			−	6.05304i		0		−18.4566				0		26.8946				0
513.12		0			−	0.324689i		0				6.05304i		0		18.4566				0		26.8946				0
513.13		0				0.324689i		0			−	6.05304i		0		18.4566				0		26.8946				0
513.14		0				0.324689i		0				6.05304i		0		−18.4566				0		26.8946				0
513.15		0				3.36468i		0			−	12.3022i		0		−15.0403				0		15.6789				0
513.16		0				3.36468i		0				12.3022i		0		15.0403				0		15.6789				0
513.17		0				4.95293i		0			−	18.5500i		0		−19.2842				0		2.46849				0
513.18		0				4.95293i		0				18.5500i		0		19.2842				0		2.46849				0
513.19		0				6.38533i		0			−	18.9781i		0		26.2604				0		−13.7725				0
513.20		0				6.38533i		0				18.9781i		0		−26.2604				0		−13.7725				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
8.b	even	2	1	inner
8.d	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1024.4.b.m		24
4.b	odd	2	1	inner	1024.4.b.m		24
8.b	even	2	1	inner	1024.4.b.m		24
8.d	odd	2	1	inner	1024.4.b.m		24
16.e	even	4	1		1024.4.a.o		12
16.e	even	4	1		1024.4.a.p		12
16.f	odd	4	1		1024.4.a.o		12
16.f	odd	4	1		1024.4.a.p		12
32.g	even	8	2		512.4.e.q	✓	24
32.g	even	8	2		512.4.e.r	yes	24
32.h	odd	8	2		512.4.e.q	✓	24
32.h	odd	8	2		512.4.e.r	yes	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
512.4.e.q	✓	24	32.g	even	8	2
512.4.e.q	✓	24	32.h	odd	8	2
512.4.e.r	yes	24	32.g	even	8	2
512.4.e.r	yes	24	32.h	odd	8	2
1024.4.a.o		12	16.e	even	4	1
1024.4.a.o		12	16.f	odd	4	1
1024.4.a.p		12	16.e	even	4	1
1024.4.a.p		12	16.f	odd	4	1
1024.4.b.m		24	1.a	even	1	1	trivial
1024.4.b.m		24	4.b	odd	2	1	inner
1024.4.b.m		24	8.b	even	2	1	inner
1024.4.b.m		24	8.d	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(1024, [\chi])\):

\( T_{3}^{12} + 216T_{3}^{10} + 16984T_{3}^{8} + 604032T_{3}^{6} + 9555648T_{3}^{4} + 52524544T_{3}^{2} + 5431808 \)

\( T_{5}^{12} + 900T_{5}^{10} + 268796T_{5}^{8} + 29243104T_{5}^{6} + 901290224T_{5}^{4} + 5664731200T_{5}^{2} + 8574760000 \)

T7^12 - 2352*T7^10 + 2133856*T7^8 - 936958976*T7^6 + 203113524224*T7^4 - 18906249216000*T7^2 + 400648785920000