Newform orbit 287.3.m.a

• Label: 287.3.m.a
• Level: $287$
• Weight: $3$
• Character orbit: 287.m
• Analytic conductor: $7.820$
• Analytic rank: $0$
• Dimension: $168$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.m (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.82018358714\)
Analytic rank:	\(0\)
Dimension:	\(168\)
Relative dimension:	\(42\) over \(\Q(\zeta_{8})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 168 q + 8 q^{2} - 16 q^{3} + 24 q^{6} - 48 q^{8} - 48 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
85.1	−2.66518	+	2.66518i	−0.402189	+	0.970969i		−	10.2064i	−1.88272	−	1.88272i	−1.51590	−	3.65972i	−1.01249	+	2.44436i	16.5412	+	16.5412i	5.58294	+	5.58294i	10.0356
85.2	−2.60935	+	2.60935i	−1.18140	+	2.85214i		−	9.61738i	5.05187	+	5.05187i	−4.35956	−	10.5249i	1.01249	−	2.44436i	14.6577	+	14.6577i	−0.375070	−	0.375070i	−26.3641
85.3	−2.53377	+	2.53377i	−2.06584	+	4.98738i		−	8.83994i	−5.28886	−	5.28886i	−7.40250	−	17.8712i	1.01249	−	2.44436i	12.2633	+	12.2633i	−14.2423	−	14.2423i	26.8015
85.4	−2.35635	+	2.35635i	0.594151	−	1.43441i		−	7.10479i	0.766826	+	0.766826i	1.97994	+	4.77999i	1.01249	−	2.44436i	7.31597	+	7.31597i	4.65945	+	4.65945i	−3.61382
85.5	−2.28855	+	2.28855i	−1.56996	+	3.79022i		−	6.47494i	1.63254	+	1.63254i	−5.08118	−	12.2670i	−1.01249	+	2.44436i	5.66404	+	5.66404i	−5.53702	−	5.53702i	−7.47229
85.6	−2.24689	+	2.24689i	1.13818	−	2.74781i		−	6.09703i	6.89996	+	6.89996i	3.61666	+	8.73139i	−1.01249	+	2.44436i	4.71181	+	4.71181i	0.108960	+	0.108960i	−31.0069
85.7	−2.09220	+	2.09220i	0.418806	−	1.01109i		−	4.75459i	−5.05847	−	5.05847i	1.23917	+	2.99162i	−1.01249	+	2.44436i	1.57875	+	1.57875i	5.51706	+	5.51706i	21.1667
85.8	−1.90333	+	1.90333i	1.37451	−	3.31835i		−	3.24533i	−1.07431	−	1.07431i	3.69978	+	8.93206i	−1.01249	+	2.44436i	−1.43639	−	1.43639i	−2.75823	−	2.75823i	4.08952
85.9	−1.74186	+	1.74186i	1.60775	−	3.88144i		−	2.06815i	−6.92683	−	6.92683i	3.96046	+	9.56139i	1.01249	−	2.44436i	−3.36502	−	3.36502i	−6.11678	−	6.11678i	24.1311
85.10	−1.67751	+	1.67751i	0.0291431	−	0.0703578i		−	1.62807i	1.99276	+	1.99276i	0.0691379	+	0.166914i	1.01249	−	2.44436i	−3.97893	−	3.97893i	6.35986	+	6.35986i	−6.68576
85.11	−1.56178	+	1.56178i	−1.33869	+	3.23188i		−	0.878306i	−2.93781	−	2.93781i	−2.95674	−	7.13821i	1.01249	−	2.44436i	−4.87540	−	4.87540i	−2.28898	−	2.28898i	9.17643
85.12	−1.53733	+	1.53733i	−1.13549	+	2.74132i		−	0.726768i	4.22119	+	4.22119i	−2.46869	−	5.95995i	−1.01249	+	2.44436i	−5.03204	−	5.03204i	0.138450	+	0.138450i	−12.9787
85.13	−1.25621	+	1.25621i	−2.14947	+	5.18928i			0.843870i	4.68795	+	4.68795i	−3.81864	−	9.21902i	1.01249	−	2.44436i	−6.08492	−	6.08492i	−15.9445	−	15.9445i	−11.7781
85.14	−1.20352	+	1.20352i	2.13250	−	5.14832i			1.10308i	0.770141	+	0.770141i	3.62959	+	8.76261i	−1.01249	+	2.44436i	−6.14166	−	6.14166i	−15.5936	−	15.5936i	−1.85376
85.15	−1.04509	+	1.04509i	1.67777	−	4.05049i			1.81559i	0.878824	+	0.878824i	2.47970	+	5.98653i	1.01249	−	2.44436i	−6.07779	−	6.07779i	−7.22761	−	7.22761i	−1.83689
85.16	−0.593548	+	0.593548i	−0.514688	+	1.24257i			3.29540i	−2.56222	−	2.56222i	−0.432031	−	1.04301i	1.01249	−	2.44436i	−4.33017	−	4.33017i	5.08489	+	5.08489i	3.04160
85.17	−0.558735	+	0.558735i	0.988435	−	2.38629i			3.37563i	−0.00806792	−	0.00806792i	0.781033	+	1.88558i	−1.01249	+	2.44436i	−4.12102	−	4.12102i	1.64657	+	1.64657i	0.00901566
85.18	−0.524382	+	0.524382i	0.375483	−	0.906495i			3.45005i	−4.83386	−	4.83386i	0.278453	+	0.672246i	−1.01249	+	2.44436i	−3.90667	−	3.90667i	5.68321	+	5.68321i	5.06958
85.19	−0.472219	+	0.472219i	−1.96830	+	4.75189i			3.55402i	−3.06808	−	3.06808i	−1.31446	−	3.17340i	−1.01249	+	2.44436i	−3.56715	−	3.56715i	−12.3423	−	12.3423i	2.89762
85.20	−0.328376	+	0.328376i	−0.752203	+	1.81598i			3.78434i	4.15285	+	4.15285i	−0.349318	−	0.843329i	−1.01249	+	2.44436i	−2.55619	−	2.55619i	3.63199	+	3.63199i	−2.72739

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
41.e	odd	8	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	287.3.m.a	✓	168
41.e	odd	8	1	inner	287.3.m.a	✓	168

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
287.3.m.a	✓	168	1.a	even	1	1	trivial
287.3.m.a	✓	168	41.e	odd	8	1	inner

Hecke kernels

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