Newform orbit 2016.2.cr.e

• Label: 2016.2.cr.e
• Level: $2016$
• Weight: $2$
• Character orbit: 2016.cr
• Analytic conductor: $16.098$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2016.cr (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(16.0978410475\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 168)
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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1297.1		0			0			0		−3.09843	−	1.78888i		0		−0.993295	−	2.45222i		0			0			0
1297.2		0			0			0		−3.08781	−	1.78275i		0		2.38336	−	1.14873i		0			0			0
1297.3		0			0			0		−2.93503	−	1.69454i		0		1.85242	+	1.88906i		0			0			0
1297.4		0			0			0		−1.98722	−	1.14732i		0		1.05630	+	2.42574i		0			0			0
1297.5		0			0			0		−1.56250	−	0.902108i		0		−2.63683	+	0.217074i		0			0			0
1297.6		0			0			0		−1.23074	−	0.710569i		0		−1.39545	+	2.24783i		0			0			0
1297.7		0			0			0		−0.586448	−	0.338586i		0		−2.23683	−	1.41301i		0			0			0
1297.8		0			0			0		−0.0402223	−	0.0232224i		0		1.97032	−	1.76574i		0			0			0
1297.9		0			0			0		0.0402223	+	0.0232224i		0		1.97032	−	1.76574i		0			0			0
1297.10		0			0			0		0.586448	+	0.338586i		0		−2.23683	−	1.41301i		0			0			0
1297.11		0			0			0		1.23074	+	0.710569i		0		−1.39545	+	2.24783i		0			0			0
1297.12		0			0			0		1.56250	+	0.902108i		0		−2.63683	+	0.217074i		0			0			0
1297.13		0			0			0		1.98722	+	1.14732i		0		1.05630	+	2.42574i		0			0			0
1297.14		0			0			0		2.93503	+	1.69454i		0		1.85242	+	1.88906i		0			0			0
1297.15		0			0			0		3.08781	+	1.78275i		0		2.38336	−	1.14873i		0			0			0
1297.16		0			0			0		3.09843	+	1.78888i		0		−0.993295	−	2.45222i		0			0			0
1873.1		0			0			0		−3.09843	+	1.78888i		0		−0.993295	+	2.45222i		0			0			0
1873.2		0			0			0		−3.08781	+	1.78275i		0		2.38336	+	1.14873i		0			0			0
1873.3		0			0			0		−2.93503	+	1.69454i		0		1.85242	−	1.88906i		0			0			0
1873.4		0			0			0		−1.98722	+	1.14732i		0		1.05630	−	2.42574i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.c	even	3	1	inner
8.b	even	2	1	inner
56.p	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2016.2.cr.e		32
3.b	odd	2	1		672.2.bk.a		32
4.b	odd	2	1		504.2.cj.e		32
7.c	even	3	1	inner	2016.2.cr.e		32
8.b	even	2	1	inner	2016.2.cr.e		32
8.d	odd	2	1		504.2.cj.e		32
12.b	even	2	1		168.2.bc.a	✓	32
21.g	even	6	1		4704.2.c.f		16
21.h	odd	6	1		672.2.bk.a		32
21.h	odd	6	1		4704.2.c.e		16
24.f	even	2	1		168.2.bc.a	✓	32
24.h	odd	2	1		672.2.bk.a		32
28.g	odd	6	1		504.2.cj.e		32
56.k	odd	6	1		504.2.cj.e		32
56.p	even	6	1	inner	2016.2.cr.e		32
84.j	odd	6	1		1176.2.c.f		16
84.n	even	6	1		168.2.bc.a	✓	32
84.n	even	6	1		1176.2.c.e		16
168.s	odd	6	1		672.2.bk.a		32
168.s	odd	6	1		4704.2.c.e		16
168.v	even	6	1		168.2.bc.a	✓	32
168.v	even	6	1		1176.2.c.e		16
168.ba	even	6	1		4704.2.c.f		16
168.be	odd	6	1		1176.2.c.f		16

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
168.2.bc.a	✓	32	12.b	even	2	1
168.2.bc.a	✓	32	24.f	even	2	1
168.2.bc.a	✓	32	84.n	even	6	1
168.2.bc.a	✓	32	168.v	even	6	1
504.2.cj.e		32	4.b	odd	2	1
504.2.cj.e		32	8.d	odd	2	1
504.2.cj.e		32	28.g	odd	6	1
504.2.cj.e		32	56.k	odd	6	1
672.2.bk.a		32	3.b	odd	2	1
672.2.bk.a		32	21.h	odd	6	1
672.2.bk.a		32	24.h	odd	2	1
672.2.bk.a		32	168.s	odd	6	1
1176.2.c.e		16	84.n	even	6	1
1176.2.c.e		16	168.v	even	6	1
1176.2.c.f		16	84.j	odd	6	1
1176.2.c.f		16	168.be	odd	6	1
2016.2.cr.e		32	1.a	even	1	1	trivial
2016.2.cr.e		32	7.c	even	3	1	inner
2016.2.cr.e		32	8.b	even	2	1	inner
2016.2.cr.e		32	56.p	even	6	1	inner
4704.2.c.e		16	21.h	odd	6	1
4704.2.c.e		16	168.s	odd	6	1
4704.2.c.f		16	21.g	even	6	1
4704.2.c.f		16	168.ba	even	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^32 - 48*T5^30 + 1402*T5^28 - 26528*T5^26 + 370859*T5^24 - 3789184*T5^22 + 29482826*T5^20 - 168147456*T5^18 + 724270609*T5^16 - 2228479968*T5^14 + 5037013168*T5^12 - 7430619264*T5^10 + 7421657792*T5^8 - 3023744000*T5^6 + 886791168*T5^4 - 1912832*T5^2 + 4096