Newform orbit 287.3.i.a

• Label: 287.3.i.a
• Level: $287$
• Weight: $3$
• Character orbit: 287.i
• 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.i (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.82018358714\)
Analytic rank:	\(0\)
Dimension:	\(108\)
Relative dimension:	\(54\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 108 q - 2 q^{2} - 106 q^{4} - 6 q^{5} + 20 q^{8} - 136 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
40.1	−1.94902	+	3.37581i	−0.674249	−	1.16783i	−5.59740	−	9.69497i	4.70200	+	2.71470i	5.25651			1.91113	−	6.73406i	28.0457			3.59078	−	6.21941i	−18.3286	+	10.5820i
40.2	−1.94902	+	3.37581i	0.674249	+	1.16783i	−5.59740	−	9.69497i	4.70200	+	2.71470i	−5.25651			−1.91113	+	6.73406i	28.0457			3.59078	−	6.21941i	−18.3286	+	10.5820i
40.3	−1.79153	+	3.10301i	−1.23268	−	2.13507i	−4.41913	−	7.65416i	−7.00807	−	4.04611i	8.83353			−6.98958	−	0.381749i	17.3357			1.46099	−	2.53050i	25.1103	−	14.4974i
40.4	−1.79153	+	3.10301i	1.23268	+	2.13507i	−4.41913	−	7.65416i	−7.00807	−	4.04611i	−8.83353			6.98958	+	0.381749i	17.3357			1.46099	−	2.53050i	25.1103	−	14.4974i
40.5	−1.75354	+	3.03722i	−2.52990	−	4.38192i	−4.14980	−	7.18766i	−1.03847	−	0.599559i	17.7451			6.93494	+	0.952149i	15.0790			−8.30079	+	14.3774i	3.64198	−	2.10270i
40.6	−1.75354	+	3.03722i	2.52990	+	4.38192i	−4.14980	−	7.18766i	−1.03847	−	0.599559i	−17.7451			−6.93494	−	0.952149i	15.0790			−8.30079	+	14.3774i	3.64198	−	2.10270i
40.7	−1.55835	+	2.69914i	−2.63338	−	4.56115i	−2.85692	−	4.94833i	4.74687	+	2.74061i	16.4149			−6.99950	+	0.0840686i	5.34153			−9.36940	+	16.2283i	−14.7946	+	8.54166i
40.8	−1.55835	+	2.69914i	2.63338	+	4.56115i	−2.85692	−	4.94833i	4.74687	+	2.74061i	−16.4149			6.99950	−	0.0840686i	5.34153			−9.36940	+	16.2283i	−14.7946	+	8.54166i
40.9	−1.50161	+	2.60086i	−0.735502	−	1.27393i	−2.50965	−	4.34684i	0.0228039	+	0.0131658i	4.41774			−1.47843	+	6.84209i	3.06116			3.41807	−	5.92028i	−0.0684849	+	0.0395398i
40.10	−1.50161	+	2.60086i	0.735502	+	1.27393i	−2.50965	−	4.34684i	0.0228039	+	0.0131658i	−4.41774			1.47843	−	6.84209i	3.06116			3.41807	−	5.92028i	−0.0684849	+	0.0395398i
40.11	−1.24731	+	2.16040i	−0.923338	−	1.59927i	−1.11156	−	1.92528i	−1.05182	−	0.607270i	4.60675			4.85778	+	5.04004i	−4.43264			2.79489	−	4.84090i	2.62389	−	1.51491i
40.12	−1.24731	+	2.16040i	0.923338	+	1.59927i	−1.11156	−	1.92528i	−1.05182	−	0.607270i	−4.60675			−4.85778	−	5.04004i	−4.43264			2.79489	−	4.84090i	2.62389	−	1.51491i
40.13	−1.19334	+	2.06692i	−0.991848	−	1.71793i	−0.848107	−	1.46896i	7.97769	+	4.60592i	4.73444			6.85435	−	1.42052i	−5.49839			2.53248	−	4.38638i	−19.0401	+	10.9928i
40.14	−1.19334	+	2.06692i	0.991848	+	1.71793i	−0.848107	−	1.46896i	7.97769	+	4.60592i	−4.73444			−6.85435	+	1.42052i	−5.49839			2.53248	−	4.38638i	−19.0401	+	10.9928i
40.15	−1.08643	+	1.88175i	−2.10629	−	3.64821i	−0.360668	−	0.624694i	−6.23743	−	3.60118i	9.15338			1.17747	−	6.90026i	−7.12409			−4.37295	+	7.57418i	13.5531	−	7.82487i
40.16	−1.08643	+	1.88175i	2.10629	+	3.64821i	−0.360668	−	0.624694i	−6.23743	−	3.60118i	−9.15338			−1.17747	+	6.90026i	−7.12409			−4.37295	+	7.57418i	13.5531	−	7.82487i
40.17	−0.736544	+	1.27573i	−1.76416	−	3.05561i	0.915005	+	1.58483i	2.30976	+	1.33354i	5.19752			−1.63087	−	6.80737i	−8.58812			−1.72450	+	2.98691i	−3.40248	+	1.96442i
40.18	−0.736544	+	1.27573i	1.76416	+	3.05561i	0.915005	+	1.58483i	2.30976	+	1.33354i	−5.19752			1.63087	+	6.80737i	−8.58812			−1.72450	+	2.98691i	−3.40248	+	1.96442i
40.19	−0.702038	+	1.21597i	−2.20646	−	3.82171i	1.01428	+	1.75679i	3.32560	+	1.92003i	6.19609			−5.26852	+	4.60898i	−8.46457			−5.23697	+	9.07071i	−4.66939	+	2.69588i
40.20	−0.702038	+	1.21597i	2.20646	+	3.82171i	1.01428	+	1.75679i	3.32560	+	1.92003i	−6.19609			5.26852	−	4.60898i	−8.46457			−5.23697	+	9.07071i	−4.66939	+	2.69588i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	287.3.i.a	✓	108
7.d	odd	6	1	inner	287.3.i.a	✓	108
41.b	even	2	1	inner	287.3.i.a	✓	108
287.i	odd	6	1	inner	287.3.i.a	✓	108

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
287.3.i.a	✓	108	1.a	even	1	1	trivial
287.3.i.a	✓	108	7.d	odd	6	1	inner
287.3.i.a	✓	108	41.b	even	2	1	inner
287.3.i.a	✓	108	287.i	odd	6	1	inner

Hecke kernels

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