Newform orbit 287.3.b.a

• Label: 287.3.b.a
• Level: $287$
• Weight: $3$
• Character orbit: 287.b
• Analytic conductor: $7.820$
• Analytic rank: $0$
• Dimension: $52$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.82018358714\)
Analytic rank:	\(0\)
Dimension:	\(52\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
83.1	−3.91995				−	3.45631i	11.3660				−	3.63802i			13.5486i	2.08600	−	6.68196i	−28.8744			−2.94610					14.2609i
83.2	−3.91995					3.45631i	11.3660					3.63802i		−	13.5486i	2.08600	+	6.68196i	−28.8744			−2.94610				−	14.2609i
83.3	−3.56913				−	1.37648i	8.73868				−	6.83538i			4.91282i	−2.60551	+	6.49702i	−16.9130			7.10532					24.3964i
83.4	−3.56913					1.37648i	8.73868					6.83538i		−	4.91282i	−2.60551	−	6.49702i	−16.9130			7.10532				−	24.3964i
83.5	−3.35920				−	4.56039i	7.28419					3.56634i			15.3193i	1.27295	+	6.88328i	−11.0323			−11.7972				−	11.9800i
83.6	−3.35920					4.56039i	7.28419				−	3.56634i		−	15.3193i	1.27295	−	6.88328i	−11.0323			−11.7972					11.9800i
83.7	−2.92667				−	4.64649i	4.56541					4.20752i			13.5988i	3.25112	−	6.19921i	−1.65478			−12.5899				−	12.3140i
83.8	−2.92667					4.64649i	4.56541				−	4.20752i		−	13.5988i	3.25112	+	6.19921i	−1.65478			−12.5899					12.3140i
83.9	−2.86582				−	0.616832i	4.21290					6.13459i			1.76773i	6.72196	+	1.95326i	−0.610133			8.61952				−	17.5806i
83.10	−2.86582					0.616832i	4.21290				−	6.13459i		−	1.76773i	6.72196	−	1.95326i	−0.610133			8.61952					17.5806i
83.11	−2.44013				−	4.97182i	1.95424				−	3.83331i			12.1319i	−6.90407	−	1.15493i	4.99192			−15.7190					9.35378i
83.12	−2.44013					4.97182i	1.95424					3.83331i		−	12.1319i	−6.90407	+	1.15493i	4.99192			−15.7190				−	9.35378i
83.13	−1.91914				−	2.33237i	−0.316896				−	6.26237i			4.47614i	−1.97015	−	6.71703i	8.28473			3.56006					12.0184i
83.14	−1.91914					2.33237i	−0.316896					6.26237i		−	4.47614i	−1.97015	+	6.71703i	8.28473			3.56006				−	12.0184i
83.15	−1.45610				−	1.32130i	−1.87978					7.87741i			1.92394i	−0.510666	−	6.98135i	8.56153			7.25417				−	11.4703i
83.16	−1.45610					1.32130i	−1.87978				−	7.87741i		−	1.92394i	−0.510666	+	6.98135i	8.56153			7.25417					11.4703i
83.17	−1.37538				−	3.94905i	−2.10832					8.96232i			5.43145i	−6.93022	+	0.985899i	8.40128			−6.59497				−	12.3266i
83.18	−1.37538					3.94905i	−2.10832				−	8.96232i		−	5.43145i	−6.93022	−	0.985899i	8.40128			−6.59497					12.3266i
83.19	−1.34917				−	3.09036i	−2.17974				−	2.40453i			4.16942i	6.89193	+	1.22527i	8.33752			−0.550339					3.24412i
83.20	−1.34917					3.09036i	−2.17974					2.40453i		−	4.16942i	6.89193	−	1.22527i	8.33752			−0.550339				−	3.24412i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	287.3.b.a	✓	52
7.b	odd	2	1	inner	287.3.b.a	✓	52

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
287.3.b.a	✓	52	1.a	even	1	1	trivial
287.3.b.a	✓	52	7.b	odd	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(287, [\chi])\).