Newform orbit 1512.2.cx.a

• Label: 1512.2.cx.a
• Level: $1512$
• Weight: $2$
• Character orbit: 1512.cx
• Analytic conductor: $12.073$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.cx (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(12.0733807856\)
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 dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 48 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
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	1512.2.cx.a		48
3.b	odd	2	1		504.2.cx.a	yes	48
4.b	odd	2	1		3024.2.df.e		48
7.d	odd	6	1		1512.2.bs.a		48
9.c	even	3	1		504.2.bs.a	✓	48
9.d	odd	6	1		1512.2.bs.a		48
12.b	even	2	1		1008.2.df.e		48
21.g	even	6	1		504.2.bs.a	✓	48
28.f	even	6	1		3024.2.ca.e		48
36.f	odd	6	1		1008.2.ca.e		48
36.h	even	6	1		3024.2.ca.e		48
63.k	odd	6	1		504.2.cx.a	yes	48
63.s	even	6	1	inner	1512.2.cx.a		48
84.j	odd	6	1		1008.2.ca.e		48
252.n	even	6	1		1008.2.df.e		48
252.bn	odd	6	1		3024.2.df.e		48

    

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

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1512, [\chi])\).