Newform orbit 576.3.q.k

• Label: 576.3.q.k
• Level: $576$
• Weight: $3$
• Character orbit: 576.q
• Analytic conductor: $15.695$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	576.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(15.6948632272\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 20 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
65.1		0		−2.97515	−	0.385370i		0		−1.15965	+	0.669525i		0		0.328661	−	0.569258i		0		8.70298	+	2.29306i		0
65.2		0		−2.75032	−	1.19821i		0		7.38813	−	4.26554i		0		−1.36942	+	2.37191i		0		6.12856	+	6.59096i		0
65.3		0		−2.29201	+	1.93564i		0		−3.32266	+	1.91834i		0		2.70775	−	4.68995i		0		1.50662	−	8.87300i		0
65.4		0		−1.46570	−	2.61758i		0		−6.92504	+	3.99817i		0		−6.10647	+	10.5767i		0		−4.70345	+	7.67317i		0
65.5		0		−0.760520	+	2.90200i		0		−0.439631	+	0.253821i		0		−6.44757	+	11.1675i		0		−7.84322	−	4.41406i		0
65.6		0		−0.322879	−	2.98257i		0		4.45884	−	2.57431i		0		1.35076	−	2.33958i		0		−8.79150	+	1.92602i		0
65.7		0		0.322879	+	2.98257i		0		4.45884	−	2.57431i		0		−1.35076	+	2.33958i		0		−8.79150	+	1.92602i		0
65.8		0		0.760520	−	2.90200i		0		−0.439631	+	0.253821i		0		6.44757	−	11.1675i		0		−7.84322	−	4.41406i		0
65.9		0		1.46570	+	2.61758i		0		−6.92504	+	3.99817i		0		6.10647	−	10.5767i		0		−4.70345	+	7.67317i		0
65.10		0		2.29201	−	1.93564i		0		−3.32266	+	1.91834i		0		−2.70775	+	4.68995i		0		1.50662	−	8.87300i		0
65.11		0		2.75032	+	1.19821i		0		7.38813	−	4.26554i		0		1.36942	−	2.37191i		0		6.12856	+	6.59096i		0
65.12		0		2.97515	+	0.385370i		0		−1.15965	+	0.669525i		0		−0.328661	+	0.569258i		0		8.70298	+	2.29306i		0
257.1		0		−2.97515	+	0.385370i		0		−1.15965	−	0.669525i		0		0.328661	+	0.569258i		0		8.70298	−	2.29306i		0
257.2		0		−2.75032	+	1.19821i		0		7.38813	+	4.26554i		0		−1.36942	−	2.37191i		0		6.12856	−	6.59096i		0
257.3		0		−2.29201	−	1.93564i		0		−3.32266	−	1.91834i		0		2.70775	+	4.68995i		0		1.50662	+	8.87300i		0
257.4		0		−1.46570	+	2.61758i		0		−6.92504	−	3.99817i		0		−6.10647	−	10.5767i		0		−4.70345	−	7.67317i		0
257.5		0		−0.760520	−	2.90200i		0		−0.439631	−	0.253821i		0		−6.44757	−	11.1675i		0		−7.84322	+	4.41406i		0
257.6		0		−0.322879	+	2.98257i		0		4.45884	+	2.57431i		0		1.35076	+	2.33958i		0		−8.79150	−	1.92602i		0
257.7		0		0.322879	−	2.98257i		0		4.45884	+	2.57431i		0		−1.35076	−	2.33958i		0		−8.79150	−	1.92602i		0
257.8		0		0.760520	+	2.90200i		0		−0.439631	−	0.253821i		0		6.44757	+	11.1675i		0		−7.84322	+	4.41406i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
9.d	odd	6	1	inner
36.h	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	576.3.q.k		24
3.b	odd	2	1		1728.3.q.l		24
4.b	odd	2	1	inner	576.3.q.k		24
8.b	even	2	1		288.3.q.a	✓	24
8.d	odd	2	1		288.3.q.a	✓	24
9.c	even	3	1		1728.3.q.l		24
9.d	odd	6	1	inner	576.3.q.k		24
12.b	even	2	1		1728.3.q.l		24
24.f	even	2	1		864.3.q.b		24
24.h	odd	2	1		864.3.q.b		24
36.f	odd	6	1		1728.3.q.l		24
36.h	even	6	1	inner	576.3.q.k		24
72.j	odd	6	1		288.3.q.a	✓	24
72.j	odd	6	1		2592.3.e.j		24
72.l	even	6	1		288.3.q.a	✓	24
72.l	even	6	1		2592.3.e.j		24
72.n	even	6	1		864.3.q.b		24
72.n	even	6	1		2592.3.e.j		24
72.p	odd	6	1		864.3.q.b		24
72.p	odd	6	1		2592.3.e.j		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
288.3.q.a	✓	24	8.b	even	2	1
288.3.q.a	✓	24	8.d	odd	2	1
288.3.q.a	✓	24	72.j	odd	6	1
288.3.q.a	✓	24	72.l	even	6	1
576.3.q.k		24	1.a	even	1	1	trivial
576.3.q.k		24	4.b	odd	2	1	inner
576.3.q.k		24	9.d	odd	6	1	inner
576.3.q.k		24	36.h	even	6	1	inner
864.3.q.b		24	24.f	even	2	1
864.3.q.b		24	24.h	odd	2	1
864.3.q.b		24	72.n	even	6	1
864.3.q.b		24	72.p	odd	6	1
1728.3.q.l		24	3.b	odd	2	1
1728.3.q.l		24	9.c	even	3	1
1728.3.q.l		24	12.b	even	2	1
1728.3.q.l		24	36.f	odd	6	1
2592.3.e.j		24	72.j	odd	6	1
2592.3.e.j		24	72.l	even	6	1
2592.3.e.j		24	72.n	even	6	1
2592.3.e.j		24	72.p	odd	6	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(576, [\chi])\):

T5^12 - 90*T5^10 + 6627*T5^8 + 5292*T5^7 - 130514*T5^6 - 159084*T5^5 + 2092761*T5^4 + 6522444*T5^3 + 7884996*T5^2 + 4056048*T5 + 839056

T7^24 + 360*T7^22 + 90234*T7^20 + 11637392*T7^18 + 1080326187*T7^16 + 40447183032*T7^14 + 1071057738570*T7^12 + 13129538346000*T7^10 + 115382889552465*T7^8 + 552691321845800*T7^6 + 1823555068431408*T7^4 + 779058694265472*T7^2 + 296043132457216