Newform orbit 576.2.s.g

• Label: 576.2.s.g
• Level: $576$
• Weight: $2$
• Character orbit: 576.s
• Analytic conductor: $4.599$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(4.59938315643\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
191.1		0		−1.71910	+	0.211392i		0		0.135038	−	0.0779642i		0		−0.349281	−	0.201658i		0		2.91063	−	0.726809i		0
191.2		0		−1.55381	−	0.765299i		0		−1.81740	+	1.04928i		0		0.143714	+	0.0829731i		0		1.82863	+	2.37826i		0
191.3		0		−1.20567	+	1.24353i		0		0.398132	−	0.229862i		0		4.28309	+	2.47284i		0		−0.0927324	−	2.99857i		0
191.4		0		−1.05094	−	1.37678i		0		3.01113	−	1.73848i		0		−3.12309	−	1.80312i		0		−0.791040	+	2.89383i		0
191.5		0		−0.683478	+	1.59150i		0		−3.40926	+	1.96834i		0		−0.961325	−	0.555021i		0		−2.06572	−	2.17550i		0
191.6		0		−0.324214	+	1.70144i		0		1.68236	−	0.971313i		0		−2.61432	−	1.50938i		0		−2.78977	−	1.10326i		0
191.7		0		0.324214	−	1.70144i		0		1.68236	−	0.971313i		0		2.61432	+	1.50938i		0		−2.78977	−	1.10326i		0
191.8		0		0.683478	−	1.59150i		0		−3.40926	+	1.96834i		0		0.961325	+	0.555021i		0		−2.06572	−	2.17550i		0
191.9		0		1.05094	+	1.37678i		0		3.01113	−	1.73848i		0		3.12309	+	1.80312i		0		−0.791040	+	2.89383i		0
191.10		0		1.20567	−	1.24353i		0		0.398132	−	0.229862i		0		−4.28309	−	2.47284i		0		−0.0927324	−	2.99857i		0
191.11		0		1.55381	+	0.765299i		0		−1.81740	+	1.04928i		0		−0.143714	−	0.0829731i		0		1.82863	+	2.37826i		0
191.12		0		1.71910	−	0.211392i		0		0.135038	−	0.0779642i		0		0.349281	+	0.201658i		0		2.91063	−	0.726809i		0
383.1		0		−1.71910	−	0.211392i		0		0.135038	+	0.0779642i		0		−0.349281	+	0.201658i		0		2.91063	+	0.726809i		0
383.2		0		−1.55381	+	0.765299i		0		−1.81740	−	1.04928i		0		0.143714	−	0.0829731i		0		1.82863	−	2.37826i		0
383.3		0		−1.20567	−	1.24353i		0		0.398132	+	0.229862i		0		4.28309	−	2.47284i		0		−0.0927324	+	2.99857i		0
383.4		0		−1.05094	+	1.37678i		0		3.01113	+	1.73848i		0		−3.12309	+	1.80312i		0		−0.791040	−	2.89383i		0
383.5		0		−0.683478	−	1.59150i		0		−3.40926	−	1.96834i		0		−0.961325	+	0.555021i		0		−2.06572	+	2.17550i		0
383.6		0		−0.324214	−	1.70144i		0		1.68236	+	0.971313i		0		−2.61432	+	1.50938i		0		−2.78977	+	1.10326i		0
383.7		0		0.324214	+	1.70144i		0		1.68236	+	0.971313i		0		2.61432	−	1.50938i		0		−2.78977	+	1.10326i		0
383.8		0		0.683478	+	1.59150i		0		−3.40926	−	1.96834i		0		0.961325	−	0.555021i		0		−2.06572	+	2.17550i		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	576.2.s.g		24
3.b	odd	2	1		1728.2.s.g		24
4.b	odd	2	1	inner	576.2.s.g		24
8.b	even	2	1		288.2.s.a	✓	24
8.d	odd	2	1		288.2.s.a	✓	24
9.c	even	3	1		1728.2.s.g		24
9.c	even	3	1		5184.2.c.m		24
9.d	odd	6	1	inner	576.2.s.g		24
9.d	odd	6	1		5184.2.c.m		24
12.b	even	2	1		1728.2.s.g		24
24.f	even	2	1		864.2.s.a		24
24.h	odd	2	1		864.2.s.a		24
36.f	odd	6	1		1728.2.s.g		24
36.f	odd	6	1		5184.2.c.m		24
36.h	even	6	1	inner	576.2.s.g		24
36.h	even	6	1		5184.2.c.m		24
72.j	odd	6	1		288.2.s.a	✓	24
72.j	odd	6	1		2592.2.c.c		24
72.l	even	6	1		288.2.s.a	✓	24
72.l	even	6	1		2592.2.c.c		24
72.n	even	6	1		864.2.s.a		24
72.n	even	6	1		2592.2.c.c		24
72.p	odd	6	1		864.2.s.a		24
72.p	odd	6	1		2592.2.c.c		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
288.2.s.a	✓	24	8.b	even	2	1
288.2.s.a	✓	24	8.d	odd	2	1
288.2.s.a	✓	24	72.j	odd	6	1
288.2.s.a	✓	24	72.l	even	6	1
576.2.s.g		24	1.a	even	1	1	trivial
576.2.s.g		24	4.b	odd	2	1	inner
576.2.s.g		24	9.d	odd	6	1	inner
576.2.s.g		24	36.h	even	6	1	inner
864.2.s.a		24	24.f	even	2	1
864.2.s.a		24	24.h	odd	2	1
864.2.s.a		24	72.n	even	6	1
864.2.s.a		24	72.p	odd	6	1
1728.2.s.g		24	3.b	odd	2	1
1728.2.s.g		24	9.c	even	3	1
1728.2.s.g		24	12.b	even	2	1
1728.2.s.g		24	36.f	odd	6	1
2592.2.c.c		24	72.j	odd	6	1
2592.2.c.c		24	72.l	even	6	1
2592.2.c.c		24	72.n	even	6	1
2592.2.c.c		24	72.p	odd	6	1
5184.2.c.m		24	9.c	even	3	1
5184.2.c.m		24	9.d	odd	6	1
5184.2.c.m		24	36.f	odd	6	1
5184.2.c.m		24	36.h	even	6	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(576, [\chi])\):

T5^12 - 18*T5^10 + 267*T5^8 - 156*T5^7 - 986*T5^6 + 684*T5^5 + 3081*T5^4 - 3420*T5^3 + 1428*T5^2 - 240*T5 + 16

T7^24 - 48*T7^22 + 1578*T7^20 - 27152*T7^18 + 338091*T7^16 - 2383368*T7^14 + 11665722*T7^12 - 15463464*T7^10 + 15637137*T7^8 - 2856440*T7^6 + 415920*T7^4 - 11136*T7^2 + 256