Newform orbit 1260.2.dq.b

• Label: 1260.2.dq.b
• Level: $1260$
• Weight: $2$
• Character orbit: 1260.dq
• Analytic conductor: $10.061$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.dq (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.0611506547\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(8\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 8 q^{7} - 12 q^{25} - 24 q^{31} - 4 q^{37} + 8 q^{43} - 24 q^{61} - 32 q^{67} - 60 q^{73} + 24 q^{85} + 88 q^{91}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
73.1		0			0			0		−2.12599	+	0.692949i		0		−2.46923	+	0.950207i		0			0			0
73.2		0			0			0		−1.33786	−	1.79168i		0		−0.921900	−	2.47994i		0			0			0
73.3		0			0			0		−1.01240	+	1.99375i		0		2.64371	−	0.103935i		0			0			0
73.4		0			0			0		−0.785053	−	2.09373i		0		−0.252577	+	2.63367i		0			0			0
73.5		0			0			0		0.785053	+	2.09373i		0		−0.252577	+	2.63367i		0			0			0
73.6		0			0			0		1.01240	−	1.99375i		0		2.64371	−	0.103935i		0			0			0
73.7		0			0			0		1.33786	+	1.79168i		0		−0.921900	−	2.47994i		0			0			0
73.8		0			0			0		2.12599	−	0.692949i		0		−2.46923	+	0.950207i		0			0			0
397.1		0			0			0		−2.12599	−	0.692949i		0		−2.46923	−	0.950207i		0			0			0
397.2		0			0			0		−1.33786	+	1.79168i		0		−0.921900	+	2.47994i		0			0			0
397.3		0			0			0		−1.01240	−	1.99375i		0		2.64371	+	0.103935i		0			0			0
397.4		0			0			0		−0.785053	+	2.09373i		0		−0.252577	−	2.63367i		0			0			0
397.5		0			0			0		0.785053	−	2.09373i		0		−0.252577	−	2.63367i		0			0			0
397.6		0			0			0		1.01240	+	1.99375i		0		2.64371	+	0.103935i		0			0			0
397.7		0			0			0		1.33786	−	1.79168i		0		−0.921900	+	2.47994i		0			0			0
397.8		0			0			0		2.12599	+	0.692949i		0		−2.46923	−	0.950207i		0			0			0
577.1		0			0			0		−2.23284	−	0.120113i		0		0.103935	+	2.64371i		0			0			0
577.2		0			0			0		−1.66310	+	1.49468i		0		−0.950207	−	2.46923i		0			0			0
577.3		0			0			0		−1.42069	−	1.72674i		0		−2.63367	−	0.252577i		0			0			0
577.4		0			0			0		−0.882709	−	2.05446i		0		2.47994	−	0.921900i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.c	odd	4	1	inner
7.d	odd	6	1	inner
15.e	even	4	1	inner
21.g	even	6	1	inner
35.k	even	12	1	inner
105.w	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1260.2.dq.b	✓	32
3.b	odd	2	1	inner	1260.2.dq.b	✓	32
5.c	odd	4	1	inner	1260.2.dq.b	✓	32
7.d	odd	6	1	inner	1260.2.dq.b	✓	32
15.e	even	4	1	inner	1260.2.dq.b	✓	32
21.g	even	6	1	inner	1260.2.dq.b	✓	32
35.k	even	12	1	inner	1260.2.dq.b	✓	32
105.w	odd	12	1	inner	1260.2.dq.b	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1260.2.dq.b	✓	32	1.a	even	1	1	trivial
1260.2.dq.b	✓	32	3.b	odd	2	1	inner
1260.2.dq.b	✓	32	5.c	odd	4	1	inner
1260.2.dq.b	✓	32	7.d	odd	6	1	inner
1260.2.dq.b	✓	32	15.e	even	4	1	inner
1260.2.dq.b	✓	32	21.g	even	6	1	inner
1260.2.dq.b	✓	32	35.k	even	12	1	inner
1260.2.dq.b	✓	32	105.w	odd	12	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T11^16 + 38*T11^14 + 1138*T11^12 + 10568*T11^10 + 73246*T11^8 + 143180*T11^6 + 204400*T11^4 + 132500*T11^2 + 62500