Newform orbit 2592.2.f.c

• Label: 2592.2.f.c
• Level: $2592$
• Weight: $2$
• Character orbit: 2592.f
• Analytic conductor: $20.697$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(20.6972242039\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	no (minimal twist has level 648)
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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1295.1		0			0			0		−3.91972				0			−	3.47231i		0			0			0
1295.2		0			0			0		−3.91972				0				3.47231i		0			0			0
1295.3		0			0			0		−3.62447				0				1.28026i		0			0			0
1295.4		0			0			0		−3.62447				0			−	1.28026i		0			0			0
1295.5		0			0			0		−1.78731				0			−	3.35928i		0			0			0
1295.6		0			0			0		−1.78731				0				3.35928i		0			0			0
1295.7		0			0			0		−1.49307				0			−	0.420546i		0			0			0
1295.8		0			0			0		−1.49307				0				0.420546i		0			0			0
1295.9		0			0			0		−1.08321				0			−	0.811362i		0			0			0
1295.10		0			0			0		−1.08321				0				0.811362i		0			0			0
1295.11		0			0			0		−0.949666				0				4.71000i		0			0			0
1295.12		0			0			0		−0.949666				0			−	4.71000i		0			0			0
1295.13		0			0			0		0.949666				0				4.71000i		0			0			0
1295.14		0			0			0		0.949666				0			−	4.71000i		0			0			0
1295.15		0			0			0		1.08321				0			−	0.811362i		0			0			0
1295.16		0			0			0		1.08321				0				0.811362i		0			0			0
1295.17		0			0			0		1.49307				0			−	0.420546i		0			0			0
1295.18		0			0			0		1.49307				0				0.420546i		0			0			0
1295.19		0			0			0		1.78731				0			−	3.35928i		0			0			0
1295.20		0			0			0		1.78731				0				3.35928i		0			0			0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2592.2.f.c		24
3.b	odd	2	1	inner	2592.2.f.c		24
4.b	odd	2	1		648.2.f.c	✓	24
8.b	even	2	1		648.2.f.c	✓	24
8.d	odd	2	1	inner	2592.2.f.c		24
9.c	even	3	2		2592.2.p.g		48
9.d	odd	6	2		2592.2.p.g		48
12.b	even	2	1		648.2.f.c	✓	24
24.f	even	2	1	inner	2592.2.f.c		24
24.h	odd	2	1		648.2.f.c	✓	24
36.f	odd	6	2		648.2.l.g		48
36.h	even	6	2		648.2.l.g		48
72.j	odd	6	2		648.2.l.g		48
72.l	even	6	2		2592.2.p.g		48
72.n	even	6	2		648.2.l.g		48
72.p	odd	6	2		2592.2.p.g		48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
648.2.f.c	✓	24	4.b	odd	2	1
648.2.f.c	✓	24	8.b	even	2	1
648.2.f.c	✓	24	12.b	even	2	1
648.2.f.c	✓	24	24.h	odd	2	1
648.2.l.g		48	36.f	odd	6	2
648.2.l.g		48	36.h	even	6	2
648.2.l.g		48	72.j	odd	6	2
648.2.l.g		48	72.n	even	6	2
2592.2.f.c		24	1.a	even	1	1	trivial
2592.2.f.c		24	3.b	odd	2	1	inner
2592.2.f.c		24	8.d	odd	2	1	inner
2592.2.f.c		24	24.f	even	2	1	inner
2592.2.p.g		48	9.c	even	3	2
2592.2.p.g		48	9.d	odd	6	2
2592.2.p.g		48	72.l	even	6	2
2592.2.p.g		48	72.p	odd	6	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{12} - 36T_{5}^{10} + 435T_{5}^{8} - 2088T_{5}^{6} + 4515T_{5}^{4} - 4356T_{5}^{2} + 1521 \) acting on \(S_{2}^{\mathrm{new}}(2592, [\chi])\).