Newform orbit 2016.3.e.c

• Label: 2016.3.e.c
• Level: $2016$
• Weight: $3$
• Character orbit: 2016.e
• Analytic conductor: $54.932$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2016.e (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(54.9320212950\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1007.1		0			0			0			−	6.99549i		0		−6.66208	+	2.14866i		0			0			0
1007.2		0			0			0				6.99549i		0		−6.66208	−	2.14866i		0			0			0
1007.3		0			0			0			−	5.14633i		0		6.42568	−	2.77681i		0			0			0
1007.4		0			0			0				5.14633i		0		6.42568	+	2.77681i		0			0			0
1007.5		0			0			0			−	9.10939i		0		0.958628	+	6.93405i		0			0			0
1007.6		0			0			0				9.10939i		0		0.958628	−	6.93405i		0			0			0
1007.7		0			0			0			−	9.10939i		0		0.958628	−	6.93405i		0			0			0
1007.8		0			0			0				9.10939i		0		0.958628	+	6.93405i		0			0			0
1007.9		0			0			0			−	5.14633i		0		−6.42568	+	2.77681i		0			0			0
1007.10		0			0			0				5.14633i		0		−6.42568	−	2.77681i		0			0			0
1007.11		0			0			0			−	4.58342i		0		3.81116	−	5.87155i		0			0			0
1007.12		0			0			0				4.58342i		0		3.81116	+	5.87155i		0			0			0
1007.13		0			0			0			−	0.489356i		0		5.24868	+	4.63156i		0			0			0
1007.14		0			0			0				0.489356i		0		5.24868	−	4.63156i		0			0			0
1007.15		0			0			0			−	3.51431i		0		−6.42922	+	2.76859i		0			0			0
1007.16		0			0			0				3.51431i		0		−6.42922	−	2.76859i		0			0			0
1007.17		0			0			0			−	3.51431i		0		6.42922	−	2.76859i		0			0			0
1007.18		0			0			0				3.51431i		0		6.42922	+	2.76859i		0			0			0
1007.19		0			0			0			−	0.489356i		0		−5.24868	−	4.63156i		0			0			0
1007.20		0			0			0				0.489356i		0		−5.24868	+	4.63156i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
7.b	odd	2	1	inner
8.d	odd	2	1	inner
21.c	even	2	1	inner
24.f	even	2	1	inner
56.e	even	2	1	inner
168.e	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2016.3.e.c		48
3.b	odd	2	1	inner	2016.3.e.c		48
4.b	odd	2	1		504.3.e.c	✓	48
7.b	odd	2	1	inner	2016.3.e.c		48
8.b	even	2	1		504.3.e.c	✓	48
8.d	odd	2	1	inner	2016.3.e.c		48
12.b	even	2	1		504.3.e.c	✓	48
21.c	even	2	1	inner	2016.3.e.c		48
24.f	even	2	1	inner	2016.3.e.c		48
24.h	odd	2	1		504.3.e.c	✓	48
28.d	even	2	1		504.3.e.c	✓	48
56.e	even	2	1	inner	2016.3.e.c		48
56.h	odd	2	1		504.3.e.c	✓	48
84.h	odd	2	1		504.3.e.c	✓	48
168.e	odd	2	1	inner	2016.3.e.c		48
168.i	even	2	1		504.3.e.c	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
504.3.e.c	✓	48	4.b	odd	2	1
504.3.e.c	✓	48	8.b	even	2	1
504.3.e.c	✓	48	12.b	even	2	1
504.3.e.c	✓	48	24.h	odd	2	1
504.3.e.c	✓	48	28.d	even	2	1
504.3.e.c	✓	48	56.h	odd	2	1
504.3.e.c	✓	48	84.h	odd	2	1
504.3.e.c	✓	48	168.i	even	2	1
2016.3.e.c		48	1.a	even	1	1	trivial
2016.3.e.c		48	3.b	odd	2	1	inner
2016.3.e.c		48	7.b	odd	2	1	inner
2016.3.e.c		48	8.d	odd	2	1	inner
2016.3.e.c		48	21.c	even	2	1	inner
2016.3.e.c		48	24.f	even	2	1	inner
2016.3.e.c		48	56.e	even	2	1	inner
2016.3.e.c		48	168.e	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{12} + 192T_{5}^{10} + 13144T_{5}^{8} + 403792T_{5}^{6} + 5643664T_{5}^{4} + 29232576T_{5}^{2} + 6682176 \) acting on \(S_{3}^{\mathrm{new}}(2016, [\chi])\).