Newform orbit 3024.2.df.e

• Label: 3024.2.df.e
• Level: $3024$
• Weight: $2$
• Character orbit: 3024.df
• Analytic conductor: $24.147$
• Analytic rank: $0$
• Dimension: $48$
• Inner twists: $2$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(24.1467615712\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(24\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 48 q^{25} - 18 q^{29} - 18 q^{31} + 6 q^{41} + 6 q^{43} + 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} - 6 q^{79} + 18 q^{89} - 6 q^{91} - 54 q^{95}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1		0			0			0		−4.11484				0		2.54819	−	0.711830i		0			0			0
17.2		0			0			0		−4.09884				0		0.146661	+	2.64168i		0			0			0
17.3		0			0			0		−3.53401				0		−1.30083	−	2.30388i		0			0			0
17.4		0			0			0		−2.76937				0		1.21939	+	2.34800i		0			0			0
17.5		0			0			0		−2.59337				0		2.61256	−	0.417759i		0			0			0
17.6		0			0			0		−2.22830				0		−2.51733	−	0.814280i		0			0			0
17.7		0			0			0		−2.20884				0		−2.16520	−	1.52049i		0			0			0
17.8		0			0			0		−2.04899				0		−1.41312	+	2.23676i		0			0			0
17.9		0			0			0		−1.36828				0		−2.64451	−	0.0810554i		0			0			0
17.10		0			0			0		0.0525740				0		−2.44149	+	1.01937i		0			0			0
17.11		0			0			0		0.203178				0		1.27132	+	2.32029i		0			0			0
17.12		0			0			0		0.207028				0		1.37075	−	2.26297i		0			0			0
17.13		0			0			0		0.542075				0		2.62378	−	0.340238i		0			0			0
17.14		0			0			0		0.623597				0		0.996837	−	2.45078i		0			0			0
17.15		0			0			0		1.05582				0		−1.79851	−	1.94045i		0			0			0
17.16		0			0			0		1.07485				0		1.26701	+	2.32265i		0			0			0
17.17		0			0			0		1.28783				0		−1.10056	+	2.40599i		0			0			0
17.18		0			0			0		1.58600				0		1.06431	−	2.42224i		0			0			0
17.19		0			0			0		1.81173				0		−1.69266	+	2.03345i		0			0			0
17.20		0			0			0		2.22094				0		2.45091	+	0.996507i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
63.s	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.df.e		48
3.b	odd	2	1		1008.2.df.e		48
4.b	odd	2	1		1512.2.cx.a		48
7.d	odd	6	1		3024.2.ca.e		48
9.c	even	3	1		1008.2.ca.e		48
9.d	odd	6	1		3024.2.ca.e		48
12.b	even	2	1		504.2.cx.a	yes	48
21.g	even	6	1		1008.2.ca.e		48
28.f	even	6	1		1512.2.bs.a		48
36.f	odd	6	1		504.2.bs.a	✓	48
36.h	even	6	1		1512.2.bs.a		48
63.k	odd	6	1		1008.2.df.e		48
63.s	even	6	1	inner	3024.2.df.e		48
84.j	odd	6	1		504.2.bs.a	✓	48
252.n	even	6	1		504.2.cx.a	yes	48
252.bn	odd	6	1		1512.2.cx.a		48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
504.2.bs.a	✓	48	36.f	odd	6	1
504.2.bs.a	✓	48	84.j	odd	6	1
504.2.cx.a	yes	48	12.b	even	2	1
504.2.cx.a	yes	48	252.n	even	6	1
1008.2.ca.e		48	9.c	even	3	1
1008.2.ca.e		48	21.g	even	6	1
1008.2.df.e		48	3.b	odd	2	1
1008.2.df.e		48	63.k	odd	6	1
1512.2.bs.a		48	28.f	even	6	1
1512.2.bs.a		48	36.h	even	6	1
1512.2.cx.a		48	4.b	odd	2	1
1512.2.cx.a		48	252.bn	odd	6	1
3024.2.ca.e		48	7.d	odd	6	1
3024.2.ca.e		48	9.d	odd	6	1
3024.2.df.e		48	1.a	even	1	1	trivial
3024.2.df.e		48	63.s	even	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 - 72*T5^22 + 12*T5^21 + 2175*T5^20 - 768*T5^19 - 36005*T5^18 + 20280*T5^17 + 357756*T5^16 - 287724*T5^15 - 2188401*T5^14 + 2387970*T5^13 + 8008817*T5^12 - 11791020*T5^11 - 15323967*T5^10 + 33359910*T5^9 + 6433746*T5^8 - 47326098*T5^7 + 23713832*T5^6 + 19294080*T5^5 - 25983819*T5^4 + 11529738*T5^3 - 2383875*T5^2 + 220260*T5 - 6476