Newform orbit 287.3.o.a

• Label: 287.3.o.a
• Level: $287$
• Weight: $3$
• Character orbit: 287.o
• Analytic conductor: $7.820$
• Analytic rank: $0$
• Dimension: $216$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.o (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.82018358714\)
Analytic rank:	\(0\)
Dimension:	\(216\)
Relative dimension:	\(54\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 216 q - 6 q^{2} - 110 q^{4} - 3 q^{7} - 2 q^{8} - 648 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
139.1	−1.19816	+	3.68755i		−	4.62584i	−8.92636	−	6.48538i	−1.55146	+	2.13541i	17.0580	+	5.54248i	−0.575786	−	6.97628i	22.0631	−	16.0298i	−12.3984			−6.01552	−	8.27966i
139.2	−1.19816	+	3.68755i			4.62584i	−8.92636	−	6.48538i	1.55146	−	2.13541i	−17.0580	−	5.54248i	−3.63473	−	5.98237i	22.0631	−	16.0298i	−12.3984			6.01552	+	8.27966i
139.3	−1.08729	+	3.34632i		−	0.232377i	−6.77961	−	4.92568i	1.40348	−	1.93173i	0.777610	+	0.252661i	−6.87163	+	1.33444i	12.4681	−	9.05858i	8.94600			4.93820	+	6.79685i
139.4	−1.08729	+	3.34632i			0.232377i	−6.77961	−	4.92568i	−1.40348	+	1.93173i	−0.777610	−	0.252661i	6.34363	−	2.95945i	12.4681	−	9.05858i	8.94600			−4.93820	−	6.79685i
139.5	−1.08527	+	3.34011i		−	1.54191i	−6.74248	−	4.89870i	−3.83280	+	5.27539i	5.15016	+	1.67339i	−0.829150	+	6.95072i	12.3145	−	8.94703i	6.62251			−13.4608	−	18.5272i
139.6	−1.08527	+	3.34011i			1.54191i	−6.74248	−	4.89870i	3.83280	−	5.27539i	−5.15016	−	1.67339i	4.75633	+	5.13589i	12.3145	−	8.94703i	6.62251			13.4608	+	18.5272i
139.7	−0.961384	+	2.95883i		−	3.57784i	−4.59437	−	3.33801i	5.23870	−	7.21045i	10.5862	+	3.43967i	−6.98907	+	0.391037i	4.22583	−	3.07025i	−3.80091			16.2981	+	22.4324i
139.8	−0.961384	+	2.95883i			3.57784i	−4.59437	−	3.33801i	−5.23870	+	7.21045i	−10.5862	−	3.43967i	5.88412	−	3.79172i	4.22583	−	3.07025i	−3.80091			−16.2981	−	22.4324i
139.9	−0.875068	+	2.69318i		−	3.79026i	−3.25142	−	2.36230i	2.82818	−	3.89266i	10.2079	+	3.31674i	6.36840	−	2.90576i	0.0434828	−	0.0315921i	−5.36606			8.00880	+	11.0232i
139.10	−0.875068	+	2.69318i			3.79026i	−3.25142	−	2.36230i	−2.82818	+	3.89266i	−10.2079	−	3.31674i	−6.86011	+	1.39244i	0.0434828	−	0.0315921i	−5.36606			−8.00880	−	11.0232i
139.11	−0.862122	+	2.65334i		−	5.31208i	−3.06088	−	2.22386i	−1.17908	+	1.62286i	14.0948	+	4.57966i	1.57310	+	6.82095i	−0.488754	+	0.355101i	−19.2182			−3.28949	−	4.52759i
139.12	−0.862122	+	2.65334i			5.31208i	−3.06088	−	2.22386i	1.17908	−	1.62286i	−14.0948	−	4.57966i	2.73659	+	6.44291i	−0.488754	+	0.355101i	−19.2182			3.28949	+	4.52759i
139.13	−0.695933	+	2.14186i		−	1.83433i	−0.867179	−	0.630043i	−0.161169	+	0.221830i	3.92888	+	1.27657i	−1.23898	−	6.88948i	−5.33494	+	3.87606i	5.63523			−0.362966	−	0.499580i
139.14	−0.695933	+	2.14186i			1.83433i	−0.867179	−	0.630043i	0.161169	−	0.221830i	−3.92888	−	1.27657i	−3.04717	−	6.30196i	−5.33494	+	3.87606i	5.63523			0.362966	+	0.499580i
139.15	−0.676052	+	2.08067i		−	3.43943i	−0.636093	−	0.462148i	−5.76773	+	7.93860i	7.15633	+	2.32523i	−4.27053	−	5.54640i	−5.68810	+	4.13265i	−2.82965			−12.6184	−	17.3677i
139.16	−0.676052	+	2.08067i			3.43943i	−0.636093	−	0.462148i	5.76773	−	7.93860i	−7.15633	−	2.32523i	0.194841	−	6.99729i	−5.68810	+	4.13265i	−2.82965			12.6184	+	17.3677i
139.17	−0.566268	+	1.74279i		−	1.14923i	0.519396	+	0.377364i	−0.885877	+	1.21931i	2.00287	+	0.650771i	−4.74322	+	5.14800i	−6.88182	+	4.99994i	7.67928			−1.62335	−	2.23436i
139.18	−0.566268	+	1.74279i			1.14923i	0.519396	+	0.377364i	0.885877	−	1.21931i	−2.00287	−	0.650771i	6.86326	+	1.37682i	−6.88182	+	4.99994i	7.67928			1.62335	+	2.23436i
139.19	−0.350708	+	1.07937i		−	2.32451i	2.19403	+	1.59406i	4.01634	−	5.52802i	2.50900	+	0.815222i	2.21612	+	6.63994i	−6.16269	+	4.47746i	3.59668			4.55820	+	6.27383i
139.20	−0.350708	+	1.07937i			2.32451i	2.19403	+	1.59406i	−4.01634	+	5.52802i	−2.50900	−	0.815222i	2.10998	+	6.67443i	−6.16269	+	4.47746i	3.59668			−4.55820	−	6.27383i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
41.d	even	5	1	inner
287.o	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	287.3.o.a	✓	216
7.b	odd	2	1	inner	287.3.o.a	✓	216
41.d	even	5	1	inner	287.3.o.a	✓	216
287.o	odd	10	1	inner	287.3.o.a	✓	216

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
287.3.o.a	✓	216	1.a	even	1	1	trivial
287.3.o.a	✓	216	7.b	odd	2	1	inner
287.3.o.a	✓	216	41.d	even	5	1	inner
287.3.o.a	✓	216	287.o	odd	10	1	inner

Hecke kernels

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