Newform orbit 1287.3.c.a

• Label: 1287.3.c.a
• Level: $1287$
• Weight: $3$
• Character orbit: 1287.c
• Analytic conductor: $35.068$
• Analytic rank: $0$
• Dimension: $80$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1287 = 3^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1287.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(35.0682100232\)
Analytic rank:	\(0\)
Dimension:	\(80\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 80 q - 176 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
287.1		−	3.99047i		0		−11.9239					9.23957i		0		−9.93186					31.6201i		0		36.8703
287.2		−	3.84587i		0		−10.7907				−	2.02416i		0		1.50096					26.1161i		0		−7.78464
287.3		−	3.81051i		0		−10.5200				−	0.160432i		0		−1.83696					24.8446i		0		−0.611327
287.4		−	3.65105i		0		−9.33019					9.46256i		0		4.63846					19.4608i		0		34.5483
287.5		−	3.58842i		0		−8.87675					0.0377220i		0		8.44913					17.4998i		0		0.135363
287.6		−	3.50727i		0		−8.30097					2.09564i		0		−0.258348					15.0847i		0		7.34998
287.7		−	3.40710i		0		−7.60831				−	8.49102i		0		7.97536					12.2938i		0		−28.9297
287.8		−	3.35085i		0		−7.22818				−	4.60317i		0		−13.4444					10.8171i		0		−15.4245
287.9		−	3.31495i		0		−6.98892					5.04784i		0		2.80139					9.90812i		0		16.7334
287.10		−	3.22389i		0		−6.39348				−	8.67079i		0		−3.21153					7.71631i		0		−27.9537
287.11		−	3.18652i		0		−6.15394					7.85823i		0		12.1312					6.86357i		0		25.0404
287.12		−	3.18616i		0		−6.15161				−	5.52457i		0		−4.76233					6.85538i		0		−17.6022
287.13		−	2.82905i		0		−4.00353					0.428709i		0		−2.55558					0.00998128i		0		1.21284
287.14		−	2.82360i		0		−3.97272				−	1.16569i		0		7.45361				−	0.0770395i		0		−3.29145
287.15		−	2.81268i		0		−3.91116					3.33119i		0		−0.139282				−	0.249886i		0		9.36956
287.16		−	2.80706i		0		−3.87961					1.35773i		0		13.7583				−	0.337932i		0		3.81123
287.17		−	2.73140i		0		−3.46054				−	8.78827i		0		12.4651				−	1.47349i		0		−24.0043
287.18		−	2.70336i		0		−3.30818					7.30805i		0		−12.2734				−	1.87025i		0		19.7563
287.19		−	2.64096i		0		−2.97465					6.72424i		0		−4.18256				−	2.70789i		0		17.7584
287.20		−	2.62751i		0		−2.90379					3.79284i		0		−11.2013				−	2.88030i		0		9.96572

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1287.3.c.a	✓	80
3.b	odd	2	1	inner	1287.3.c.a	✓	80

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1287.3.c.a	✓	80	1.a	even	1	1	trivial
1287.3.c.a	✓	80	3.b	odd	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1287, [\chi])\).