Newform orbit 280.3.bb.a

• Label: 280.3.bb.a
• Level: $280$
• Weight: $3$
• Character orbit: 280.bb
• Analytic conductor: $7.629$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	280.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.62944740209\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(24\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 80 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
89.1		0		−2.91750	−	5.05326i		0		−0.0836587	+	4.99930i		0		6.99615	+	0.232281i		0		−12.5236	+	21.6916i		0
89.2		0		−2.73863	−	4.74344i		0		−3.09454	−	3.92732i		0		−0.425656	−	6.98705i		0		−10.5002	+	18.1868i		0
89.3		0		−2.59576	−	4.49598i		0		4.38195	+	2.40801i		0		−5.96958	+	3.65570i		0		−8.97591	+	15.5467i		0
89.4		0		−1.68061	−	2.91090i		0		4.65729	−	1.81926i		0		−2.84918	−	6.39392i		0		−1.14888	+	1.98992i		0
89.5		0		−1.67589	−	2.90272i		0		−4.73248	−	1.61358i		0		−6.90353	+	1.15813i		0		−1.11718	+	1.93502i		0
89.6		0		−1.61812	−	2.80267i		0		3.90393	−	3.12399i		0		6.67521	+	2.10752i		0		−0.736635	+	1.27589i		0
89.7		0		−1.35575	−	2.34822i		0		−2.85956	−	4.10158i		0		6.80912	+	1.62356i		0		0.823894	−	1.42703i		0
89.8		0		−1.32183	−	2.28948i		0		−4.80693	+	1.37603i		0		0.744948	+	6.96025i		0		1.00552	−	1.74161i		0
89.9		0		−1.12385	−	1.94656i		0		−2.80672	+	4.13791i		0		3.40477	−	6.11617i		0		1.97394	−	3.41897i		0
89.10		0		−1.00123	−	1.73417i		0		0.232261	+	4.99460i		0		−5.25223	+	4.62753i		0		2.49509	−	4.32163i		0
89.11		0		−0.375998	−	0.651248i		0		0.561892	−	4.96833i		0		−4.13893	+	5.64529i		0		4.21725	−	7.30449i		0
89.12		0		−0.0815285	−	0.141211i		0		3.57299	+	3.49768i		0		−5.16467	−	4.72505i		0		4.48671	−	7.77120i		0
89.13		0		0.0815285	+	0.141211i		0		4.81557	+	1.34546i		0		5.16467	+	4.72505i		0		4.48671	−	7.77120i		0
89.14		0		0.375998	+	0.651248i		0		−4.02175	+	2.97078i		0		4.13893	−	5.64529i		0		4.21725	−	7.30449i		0
89.15		0		1.00123	+	1.73417i		0		4.44158	−	2.29616i		0		5.25223	−	4.62753i		0		2.49509	−	4.32163i		0
89.16		0		1.12385	+	1.94656i		0		2.18018	−	4.49965i		0		−3.40477	+	6.11617i		0		1.97394	−	3.41897i		0
89.17		0		1.32183	+	2.28948i		0		−1.21178	−	4.85094i		0		−0.744948	−	6.96025i		0		1.00552	−	1.74161i		0
89.18		0		1.35575	+	2.34822i		0		−4.98185	−	0.425664i		0		−6.80912	−	1.62356i		0		0.823894	−	1.42703i		0
89.19		0		1.61812	+	2.80267i		0		−0.753495	+	4.94290i		0		−6.67521	−	2.10752i		0		−0.736635	+	1.27589i		0
89.20		0		1.67589	+	2.90272i		0		−3.76364	−	3.29166i		0		6.90353	−	1.15813i		0		−1.11718	+	1.93502i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
7.d	odd	6	1	inner
35.i	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	280.3.bb.a	✓	48
4.b	odd	2	1		560.3.br.d		48
5.b	even	2	1	inner	280.3.bb.a	✓	48
7.d	odd	6	1	inner	280.3.bb.a	✓	48
20.d	odd	2	1		560.3.br.d		48
28.f	even	6	1		560.3.br.d		48
35.i	odd	6	1	inner	280.3.bb.a	✓	48
140.s	even	6	1		560.3.br.d		48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
280.3.bb.a	✓	48	1.a	even	1	1	trivial
280.3.bb.a	✓	48	5.b	even	2	1	inner
280.3.bb.a	✓	48	7.d	odd	6	1	inner
280.3.bb.a	✓	48	35.i	odd	6	1	inner
560.3.br.d		48	4.b	odd	2	1
560.3.br.d		48	20.d	odd	2	1
560.3.br.d		48	28.f	even	6	1
560.3.br.d		48	140.s	even	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(280, [\chi])\).