Newform orbit 1404.2.cj.a

• Label: 1404.2.cj.a
• Level: $1404$
• Weight: $2$
• Character orbit: 1404.cj
• Analytic conductor: $11.211$
• Analytic rank: $0$
• Dimension: $56$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1404 = 2^{2} \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1404.cj (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.2109964438\)
Analytic rank:	\(0\)
Dimension:	\(56\)
Relative dimension:	\(14\) over \(\Q(\zeta_{12})\)
Twist minimal:	no (minimal twist has level 468)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 56 q - 2 q^{7} + 12 q^{11} + 4 q^{19} - 4 q^{31} - 4 q^{37} - 24 q^{41} - 66 q^{47} + 78 q^{65} - 14 q^{67} + 28 q^{73} - 24 q^{79} + 78 q^{83} + 36 q^{85} - 8 q^{91} + 26 q^{97}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
125.1		0			0			0		−0.939546	−	3.50643i		0		3.22796	+	0.864930i		0			0			0
125.2		0			0			0		−0.761717	−	2.84277i		0		−4.33311	−	1.16105i		0			0			0
125.3		0			0			0		−0.734125	−	2.73979i		0		1.89332	+	0.507313i		0			0			0
125.4		0			0			0		−0.698570	−	2.60710i		0		−2.01531	−	0.539999i		0			0			0
125.5		0			0			0		−0.262980	−	0.981455i		0		1.00815	+	0.270133i		0			0			0
125.6		0			0			0		−0.249888	−	0.932593i		0		−2.28503	−	0.612271i		0			0			0
125.7		0			0			0		−0.105017	−	0.391929i		0		4.28414	+	1.14793i		0			0			0
125.8		0			0			0		0.0369853	+	0.138031i		0		−3.61332	−	0.968186i		0			0			0
125.9		0			0			0		0.154104	+	0.575123i		0		0.0907757	+	0.0243233i		0			0			0
125.10		0			0			0		0.306901	+	1.14537i		0		−0.129681	−	0.0347480i		0			0			0
125.11		0			0			0		0.399894	+	1.49243i		0		3.92036	+	1.05046i		0			0			0
125.12		0			0			0		0.941608	+	3.51413i		0		0.592998	+	0.158893i		0			0			0
125.13		0			0			0		0.953715	+	3.55931i		0		−0.238284	−	0.0638481i		0			0			0
125.14		0			0			0		0.958637	+	3.57768i		0		−3.76900	−	1.00990i		0			0			0
629.1		0			0			0		−0.939546	+	3.50643i		0		3.22796	−	0.864930i		0			0			0
629.2		0			0			0		−0.761717	+	2.84277i		0		−4.33311	+	1.16105i		0			0			0
629.3		0			0			0		−0.734125	+	2.73979i		0		1.89332	−	0.507313i		0			0			0
629.4		0			0			0		−0.698570	+	2.60710i		0		−2.01531	+	0.539999i		0			0			0
629.5		0			0			0		−0.262980	+	0.981455i		0		1.00815	−	0.270133i		0			0			0
629.6		0			0			0		−0.249888	+	0.932593i		0		−2.28503	+	0.612271i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.d	odd	6	1	inner
13.d	odd	4	1	inner
117.z	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1404.2.cj.a		56
3.b	odd	2	1		468.2.cg.a	✓	56
9.c	even	3	1		468.2.cg.a	✓	56
9.d	odd	6	1	inner	1404.2.cj.a		56
13.d	odd	4	1	inner	1404.2.cj.a		56
39.f	even	4	1		468.2.cg.a	✓	56
117.y	odd	12	1		468.2.cg.a	✓	56
117.z	even	12	1	inner	1404.2.cj.a		56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
468.2.cg.a	✓	56	3.b	odd	2	1
468.2.cg.a	✓	56	9.c	even	3	1
468.2.cg.a	✓	56	39.f	even	4	1
468.2.cg.a	✓	56	117.y	odd	12	1
1404.2.cj.a		56	1.a	even	1	1	trivial
1404.2.cj.a		56	9.d	odd	6	1	inner
1404.2.cj.a		56	13.d	odd	4	1	inner
1404.2.cj.a		56	117.z	even	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1404, [\chi])\).