Newform orbit 287.3.g.a

• Label: 287.3.g.a
• Level: $287$
• Weight: $3$
• Character orbit: 287.g
• Analytic conductor: $7.820$
• Analytic rank: $0$
• Dimension: $108$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.82018358714\)
Analytic rank:	\(0\)
Dimension:	\(108\)
Relative dimension:	\(54\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 108 q - 216 q^{4} - 2 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
132.1		−	3.88864i	−1.07444	+	1.07444i	−11.1215			6.46442			4.17812	+	4.17812i	−6.77652	+	1.75466i			27.6932i			6.69115i		−	25.1378i
132.2		−	3.88864i	1.07444	−	1.07444i	−11.1215			−6.46442			−4.17812	−	4.17812i	1.75466	−	6.77652i			27.6932i			6.69115i			25.1378i
132.3		−	3.66303i	−3.03803	+	3.03803i	−9.41780			−7.09262			11.1284	+	11.1284i	1.44819	+	6.84856i			19.8456i		−	9.45930i			25.9805i
132.4		−	3.66303i	3.03803	−	3.03803i	−9.41780			7.09262			−11.1284	−	11.1284i	6.84856	+	1.44819i			19.8456i		−	9.45930i		−	25.9805i
132.5		−	3.39532i	−3.29534	+	3.29534i	−7.52821			3.85237			11.1888	+	11.1888i	3.61480	−	5.99443i			11.9794i		−	12.7186i		−	13.0800i
132.6		−	3.39532i	3.29534	−	3.29534i	−7.52821			−3.85237			−11.1888	−	11.1888i	−5.99443	+	3.61480i			11.9794i		−	12.7186i			13.0800i
132.7		−	3.19098i	−0.547162	+	0.547162i	−6.18236			3.96088			1.74598	+	1.74598i	6.79862	+	1.66698i			6.96386i			8.40123i		−	12.6391i
132.8		−	3.19098i	0.547162	−	0.547162i	−6.18236			−3.96088			−1.74598	−	1.74598i	1.66698	+	6.79862i			6.96386i			8.40123i			12.6391i
132.9		−	2.69918i	−0.291651	+	0.291651i	−3.28560			−0.108748			0.787221	+	0.787221i	−6.97500	+	0.591083i		−	1.92831i			8.82988i			0.293532i
132.10		−	2.69918i	0.291651	−	0.291651i	−3.28560			0.108748			−0.787221	−	0.787221i	0.591083	−	6.97500i		−	1.92831i			8.82988i		−	0.293532i
132.11		−	2.66341i	−2.47686	+	2.47686i	−3.09375			−7.32409			6.59690	+	6.59690i	−3.35766	−	6.14216i		−	2.41372i		−	3.26970i			19.5070i
132.12		−	2.66341i	2.47686	−	2.47686i	−3.09375			7.32409			−6.59690	−	6.59690i	−6.14216	−	3.35766i		−	2.41372i		−	3.26970i		−	19.5070i
132.13		−	2.64775i	−3.79352	+	3.79352i	−3.01059			1.69265			10.0443	+	10.0443i	−5.12305	+	4.77016i		−	2.61971i		−	19.7816i		−	4.48173i
132.14		−	2.64775i	3.79352	−	3.79352i	−3.01059			−1.69265			−10.0443	−	10.0443i	4.77016	−	5.12305i		−	2.61971i		−	19.7816i			4.48173i
132.15		−	1.73155i	−2.85212	+	2.85212i	1.00173			4.47811			4.93859	+	4.93859i	4.16852	+	5.62348i		−	8.66075i		−	7.26914i		−	7.75408i
132.16		−	1.73155i	2.85212	−	2.85212i	1.00173			−4.47811			−4.93859	−	4.93859i	5.62348	+	4.16852i		−	8.66075i		−	7.26914i			7.75408i
132.17		−	1.66337i	−2.23909	+	2.23909i	1.23319			−6.64247			3.72444	+	3.72444i	6.99925	−	0.102623i		−	8.70475i		−	1.02704i			11.0489i
132.18		−	1.66337i	2.23909	−	2.23909i	1.23319			6.64247			−3.72444	−	3.72444i	−0.102623	+	6.99925i		−	8.70475i		−	1.02704i		−	11.0489i
132.19		−	1.34555i	−2.45356	+	2.45356i	2.18949			9.16655			3.30139	+	3.30139i	−4.09097	−	5.68014i		−	8.32828i		−	3.03988i		−	12.3341i
132.20		−	1.34555i	2.45356	−	2.45356i	2.18949			−9.16655			−3.30139	−	3.30139i	−5.68014	−	4.09097i		−	8.32828i		−	3.03988i			12.3341i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
41.c	even	4	1	inner
287.g	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	287.3.g.a	✓	108
7.b	odd	2	1	inner	287.3.g.a	✓	108
41.c	even	4	1	inner	287.3.g.a	✓	108
287.g	odd	4	1	inner	287.3.g.a	✓	108

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
287.3.g.a	✓	108	1.a	even	1	1	trivial
287.3.g.a	✓	108	7.b	odd	2	1	inner
287.3.g.a	✓	108	41.c	even	4	1	inner
287.3.g.a	✓	108	287.g	odd	4	1	inner

Hecke kernels

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