Newform orbit 1512.2.bs.a

• Label: 1512.2.bs.a
• Level: $1512$
• Weight: $2$
• Character orbit: 1512.bs
• 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.bs (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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
521.1		0			0			0		−2.05742	+	3.56356i		0		1.89056	+	1.85089i		0			0			0
521.2		0			0			0		−2.04942	+	3.54970i		0		−2.21443	+	1.44785i		0			0			0
521.3		0			0			0		−1.76701	+	3.06054i		0		1.34480	−	2.27849i		0			0			0
521.4		0			0			0		−1.38468	+	2.39834i		0		−1.42373	+	2.23002i		0			0			0
521.5		0			0			0		−1.29668	+	2.24592i		0		1.66807	+	2.05367i		0			0			0
521.6		0			0			0		−1.11415	+	1.92977i		0		−0.553477	−	2.58721i		0			0			0
521.7		0			0			0		−1.10442	+	1.91291i		0		0.234181	−	2.63537i		0			0			0
521.8		0			0			0		−1.02449	+	1.77447i		0		−2.64365	−	0.105420i		0			0			0
521.9		0			0			0		−0.684139	+	1.18496i		0		−1.25206	−	2.33074i		0			0			0
521.10		0			0			0		0.0262870	−	0.0455305i		0		−2.10354	−	1.60471i		0			0			0
521.11		0			0			0		0.101589	−	0.175958i		0		−1.37377	+	2.26114i		0			0			0
521.12		0			0			0		0.103514	−	0.179292i		0		2.64517	+	0.0556151i		0			0			0
521.13		0			0			0		0.271038	−	0.469451i		0		1.60655	+	2.10214i		0			0			0
521.14		0			0			0		0.311798	−	0.540051i		0		2.62086	−	0.362103i		0			0			0
521.15		0			0			0		0.527910	−	0.914367i		0		0.781227	−	2.52778i		0			0			0
521.16		0			0			0		0.537427	−	0.930850i		0		−1.37797	+	2.25858i		0			0			0
521.17		0			0			0		0.643917	−	1.11530i		0		−2.63392	+	0.249885i		0			0			0
521.18		0			0			0		0.793002	−	1.37352i		0		2.62988	−	0.289398i		0			0			0
521.19		0			0			0		0.905867	−	1.56901i		0		−2.60735	−	0.449161i		0			0			0
521.20		0			0			0		1.11047	−	1.92339i		0		0.362456	+	2.62081i		0			0			0

Inner twists

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

    

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

Hecke kernels

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