Newform orbit 576.3.q.l

• Label: 576.3.q.l
• 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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 12 q^{9}+O(q^{10}) \)

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		−2.81202	−	1.04524i		0		−5.41309	+	3.12525i		0		3.74855	−	6.49268i		0		6.81493	+	5.87850i		0
65.2		0		−2.74879	+	1.20172i		0		3.57322	−	2.06300i		0		−5.28363	+	9.15151i		0		6.11174	−	6.60656i		0
65.3		0		−2.56384	+	1.55780i		0		6.30146	−	3.63815i		0		4.46892	−	7.74039i		0		4.14654	−	7.98788i		0
65.4		0		−1.92817	+	2.29830i		0		−7.02261	+	4.05450i		0		−1.65619	+	2.86860i		0		−1.56434	−	8.86300i		0
65.5		0		−1.65353	−	2.50317i		0		0.721152	−	0.416357i		0		1.26051	−	2.18326i		0		−3.53169	+	8.27811i		0
65.6		0		−0.106831	−	2.99810i		0		1.83987	−	1.06225i		0		−3.42470	+	5.93176i		0		−8.97717	+	0.640577i		0
65.7		0		0.106831	+	2.99810i		0		1.83987	−	1.06225i		0		3.42470	−	5.93176i		0		−8.97717	+	0.640577i		0
65.8		0		1.65353	+	2.50317i		0		0.721152	−	0.416357i		0		−1.26051	+	2.18326i		0		−3.53169	+	8.27811i		0
65.9		0		1.92817	−	2.29830i		0		−7.02261	+	4.05450i		0		1.65619	−	2.86860i		0		−1.56434	−	8.86300i		0
65.10		0		2.56384	−	1.55780i		0		6.30146	−	3.63815i		0		−4.46892	+	7.74039i		0		4.14654	−	7.98788i		0
65.11		0		2.74879	−	1.20172i		0		3.57322	−	2.06300i		0		5.28363	−	9.15151i		0		6.11174	−	6.60656i		0
65.12		0		2.81202	+	1.04524i		0		−5.41309	+	3.12525i		0		−3.74855	+	6.49268i		0		6.81493	+	5.87850i		0
257.1		0		−2.81202	+	1.04524i		0		−5.41309	−	3.12525i		0		3.74855	+	6.49268i		0		6.81493	−	5.87850i		0
257.2		0		−2.74879	−	1.20172i		0		3.57322	+	2.06300i		0		−5.28363	−	9.15151i		0		6.11174	+	6.60656i		0
257.3		0		−2.56384	−	1.55780i		0		6.30146	+	3.63815i		0		4.46892	+	7.74039i		0		4.14654	+	7.98788i		0
257.4		0		−1.92817	−	2.29830i		0		−7.02261	−	4.05450i		0		−1.65619	−	2.86860i		0		−1.56434	+	8.86300i		0
257.5		0		−1.65353	+	2.50317i		0		0.721152	+	0.416357i		0		1.26051	+	2.18326i		0		−3.53169	−	8.27811i		0
257.6		0		−0.106831	+	2.99810i		0		1.83987	+	1.06225i		0		−3.42470	−	5.93176i		0		−8.97717	−	0.640577i		0
257.7		0		0.106831	−	2.99810i		0		1.83987	+	1.06225i		0		3.42470	+	5.93176i		0		−8.97717	−	0.640577i		0
257.8		0		1.65353	−	2.50317i		0		0.721152	+	0.416357i		0		−1.26051	−	2.18326i		0		−3.53169	−	8.27811i		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.l		24
3.b	odd	2	1		1728.3.q.k		24
4.b	odd	2	1	inner	576.3.q.l		24
8.b	even	2	1		288.3.q.b	✓	24
8.d	odd	2	1		288.3.q.b	✓	24
9.c	even	3	1		1728.3.q.k		24
9.d	odd	6	1	inner	576.3.q.l		24
12.b	even	2	1		1728.3.q.k		24
24.f	even	2	1		864.3.q.a		24
24.h	odd	2	1		864.3.q.a		24
36.f	odd	6	1		1728.3.q.k		24
36.h	even	6	1	inner	576.3.q.l		24
72.j	odd	6	1		288.3.q.b	✓	24
72.j	odd	6	1		2592.3.e.i		24
72.l	even	6	1		288.3.q.b	✓	24
72.l	even	6	1		2592.3.e.i		24
72.n	even	6	1		864.3.q.a		24
72.n	even	6	1		2592.3.e.i		24
72.p	odd	6	1		864.3.q.a		24
72.p	odd	6	1		2592.3.e.i		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
288.3.q.b	✓	24	8.b	even	2	1
288.3.q.b	✓	24	8.d	odd	2	1
288.3.q.b	✓	24	72.j	odd	6	1
288.3.q.b	✓	24	72.l	even	6	1
576.3.q.l		24	1.a	even	1	1	trivial
576.3.q.l		24	4.b	odd	2	1	inner
576.3.q.l		24	9.d	odd	6	1	inner
576.3.q.l		24	36.h	even	6	1	inner
864.3.q.a		24	24.f	even	2	1
864.3.q.a		24	24.h	odd	2	1
864.3.q.a		24	72.n	even	6	1
864.3.q.a		24	72.p	odd	6	1
1728.3.q.k		24	3.b	odd	2	1
1728.3.q.k		24	9.c	even	3	1
1728.3.q.k		24	12.b	even	2	1
1728.3.q.k		24	36.f	odd	6	1
2592.3.e.i		24	72.j	odd	6	1
2592.3.e.i		24	72.l	even	6	1
2592.3.e.i		24	72.n	even	6	1
2592.3.e.i		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 + 6291*T5^8 - 7956*T5^7 - 157394*T5^6 + 325620*T5^5 + 3020121*T5^4 - 14913396*T5^3 + 27524340*T5^2 - 22192848*T5 + 7246864

T7^24 + 312*T7^22 + 60858*T7^20 + 7407504*T7^18 + 660555243*T7^16 + 41595731064*T7^14 + 1958727234186*T7^12 + 63711282291840*T7^10 + 1472167650207825*T7^8 + 19026736244001000*T7^6 + 174331200605310000*T7^4 + 831519160650000000*T7^2 + 2690420062500000000