Newform orbit 3024.2.bf.i

• Label: 3024.2.bf.i
• Level: $3024$
• Weight: $2$
• Character orbit: 3024.bf
• Analytic conductor: $24.147$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.bf (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(24.1467615712\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 1008)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1711.1		0			0			0			−	4.29566i		0		−0.334043	+	2.62458i		0			0			0
1711.2		0			0			0			−	4.29566i		0		0.334043	−	2.62458i		0			0			0
1711.3		0			0			0			−	2.39618i		0		−2.35781	+	1.20030i		0			0			0
1711.4		0			0			0			−	2.39618i		0		2.35781	−	1.20030i		0			0			0
1711.5		0			0			0			−	1.09736i		0		1.10288	+	2.40492i		0			0			0
1711.6		0			0			0			−	1.09736i		0		−1.10288	−	2.40492i		0			0			0
1711.7		0			0			0			−	0.618621i		0		1.03639	−	2.43431i		0			0			0
1711.8		0			0			0			−	0.618621i		0		−1.03639	+	2.43431i		0			0			0
1711.9		0			0			0				0.435427i		0		2.49096	+	0.891704i		0			0			0
1711.10		0			0			0				0.435427i		0		−2.49096	−	0.891704i		0			0			0
1711.11		0			0			0				2.22064i		0		−0.517968	−	2.59455i		0			0			0
1711.12		0			0			0				2.22064i		0		0.517968	+	2.59455i		0			0			0
1711.13		0			0			0				2.34835i		0		−2.61922	+	0.373730i		0			0			0
1711.14		0			0			0				2.34835i		0		2.61922	−	0.373730i		0			0			0
1711.15		0			0			0				3.40340i		0		2.63727	+	0.211643i		0			0			0
1711.16		0			0			0				3.40340i		0		−2.63727	−	0.211643i		0			0			0
2287.1		0			0			0			−	3.40340i		0		−2.63727	+	0.211643i		0			0			0
2287.2		0			0			0			−	3.40340i		0		2.63727	−	0.211643i		0			0			0
2287.3		0			0			0			−	2.34835i		0		2.61922	+	0.373730i		0			0			0
2287.4		0			0			0			−	2.34835i		0		−2.61922	−	0.373730i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
63.k	odd	6	1	inner
252.n	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3024.2.bf.i		32
3.b	odd	2	1		1008.2.bf.i	✓	32
4.b	odd	2	1	inner	3024.2.bf.i		32
7.d	odd	6	1		3024.2.cz.i		32
9.c	even	3	1		3024.2.cz.i		32
9.d	odd	6	1		1008.2.cz.i	yes	32
12.b	even	2	1		1008.2.bf.i	✓	32
21.g	even	6	1		1008.2.cz.i	yes	32
28.f	even	6	1		3024.2.cz.i		32
36.f	odd	6	1		3024.2.cz.i		32
36.h	even	6	1		1008.2.cz.i	yes	32
63.k	odd	6	1	inner	3024.2.bf.i		32
63.s	even	6	1		1008.2.bf.i	✓	32
84.j	odd	6	1		1008.2.cz.i	yes	32
252.n	even	6	1	inner	3024.2.bf.i		32
252.bn	odd	6	1		1008.2.bf.i	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1008.2.bf.i	✓	32	3.b	odd	2	1
1008.2.bf.i	✓	32	12.b	even	2	1
1008.2.bf.i	✓	32	63.s	even	6	1
1008.2.bf.i	✓	32	252.bn	odd	6	1
1008.2.cz.i	yes	32	9.d	odd	6	1
1008.2.cz.i	yes	32	21.g	even	6	1
1008.2.cz.i	yes	32	36.h	even	6	1
1008.2.cz.i	yes	32	84.j	odd	6	1
3024.2.bf.i		32	1.a	even	1	1	trivial
3024.2.bf.i		32	4.b	odd	2	1	inner
3024.2.bf.i		32	63.k	odd	6	1	inner
3024.2.bf.i		32	252.n	even	6	1	inner
3024.2.cz.i		32	7.d	odd	6	1
3024.2.cz.i		32	9.c	even	3	1
3024.2.cz.i		32	28.f	even	6	1
3024.2.cz.i		32	36.f	odd	6	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(3024, [\chi])\):

\( T_{5}^{16} + 48T_{5}^{14} + 870T_{5}^{12} + 7668T_{5}^{10} + 35001T_{5}^{8} + 79623T_{5}^{6} + 77598T_{5}^{4} + 27459T_{5}^{2} + 2916 \)

T19^32 + 146*T19^30 + 13545*T19^28 + 760432*T19^26 + 30956012*T19^24 + 845979156*T19^22 + 16893351658*T19^20 + 222174856073*T19^18 + 2123080156881*T19^16 + 13568320720637*T19^14 + 63461754167551*T19^12 + 201507658294401*T19^10 + 467691031020623*T19^8 + 708552483556510*T19^6 + 756448345289502*T19^4 + 420676341693578*T19^2 + 156863626279441