Newform orbit 287.2.w.a

• Label: 287.2.w.a
• Level: $287$
• Weight: $2$
• Character orbit: 287.w
• Analytic conductor: $2.292$
• Analytic rank: $0$
• Dimension: $208$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.w (of order \(24\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.29170653801\)
Analytic rank:	\(0\)
Dimension:	\(208\)
Relative dimension:	\(26\) over \(\Q(\zeta_{24})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 208 q - 4 q^{2} - 12 q^{3} - 12 q^{5} - 8 q^{7} - 32 q^{8} + 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−2.56100	−	0.686218i	−0.904761	+	0.694247i	4.35578	+	2.51481i	−1.05700	−	0.283223i	2.79350	−	1.15711i	−0.803969	+	2.52064i	−5.67989	−	5.67989i	−0.439844	+	1.64152i	2.51263	+	1.45067i
3.2	−2.46478	−	0.660435i	2.16154	−	1.65861i	3.90691	+	2.25565i	1.76092	+	0.471838i	−6.42311	+	2.66054i	−2.53259	−	0.765512i	−4.53126	−	4.53126i	1.14481	−	4.27250i	−4.02867	−	2.32595i
3.3	−2.32636	−	0.623346i	−0.340938	+	0.261611i	3.29134	+	1.90025i	4.19521	+	1.12410i	0.956220	−	0.396079i	2.58749	−	0.552173i	−3.06629	−	3.06629i	−0.728659	+	2.71939i	−9.05885	−	5.23013i
3.4	−2.09048	−	0.560141i	−2.51477	+	1.92965i	2.32428	+	1.34192i	−1.10540	−	0.296191i	6.33795	−	2.62527i	2.23358	−	1.41814i	−1.04651	−	1.04651i	1.82407	−	6.80751i	2.14490	+	1.23836i
3.5	−2.05371	−	0.550290i	0.683558	−	0.524512i	2.18286	+	1.26027i	−3.50008	−	0.937845i	−1.69246	+	0.701041i	−1.22753	−	2.34375i	−0.782599	−	0.782599i	−0.584319	+	2.18071i	6.67207	+	3.85212i
3.6	−1.67812	−	0.449651i	−1.39067	+	1.06710i	0.881854	+	0.509138i	0.769944	+	0.206306i	2.81353	−	1.16540i	−2.27419	−	1.35207i	1.20602	+	1.20602i	0.0188054	−	0.0701826i	−1.19929	−	0.692412i
3.7	−1.58699	−	0.425234i	0.715707	−	0.549181i	0.605675	+	0.349687i	1.24836	+	0.334498i	−1.36935	+	0.567204i	−0.971735	+	2.46084i	1.51102	+	1.51102i	−0.565821	+	2.11167i	−1.83890	−	1.06169i
3.8	−1.42899	−	0.382896i	0.0385589	−	0.0295873i	0.163340	+	0.0943042i	−1.31495	−	0.352339i	−0.0664289	+	0.0275158i	2.51506	−	0.821255i	1.89488	+	1.89488i	−0.775846	+	2.89550i	1.74413	+	1.00697i
3.9	−1.05419	−	0.282470i	2.06157	−	1.58190i	−0.700516	−	0.404443i	1.89345	+	0.507348i	−2.62013	+	1.08530i	1.12649	−	2.39395i	2.16768	+	2.16768i	0.971213	−	3.62462i	−1.85275	−	1.06969i
3.10	−0.866669	−	0.232223i	2.43423	−	1.86785i	−1.03486	−	0.597479i	−3.67938	−	0.985886i	−2.54343	+	1.05352i	−1.65100	+	2.06741i	2.02703	+	2.02703i	1.66016	−	6.19579i	2.95985	+	1.70887i
3.11	−0.626707	−	0.167926i	−2.18400	+	1.67584i	−1.36749	−	0.789519i	−2.76165	−	0.739982i	1.65015	−	0.683514i	−2.20483	+	1.46244i	1.64200	+	1.64200i	1.18496	−	4.42232i	1.60648	+	0.927504i
3.12	−0.389415	−	0.104344i	−0.138074	+	0.105948i	−1.59129	−	0.918734i	−2.37555	−	0.636527i	0.0648230	−	0.0268506i	2.38380	+	1.14782i	1.09395	+	1.09395i	−0.768618	+	2.86852i	0.858659	+	0.495747i
3.13	−0.376036	−	0.100759i	−2.29715	+	1.76267i	−1.60080	−	0.924222i	2.43497	+	0.652448i	1.04142	−	0.431369i	1.44457	+	2.21658i	1.05939	+	1.05939i	1.39346	−	5.20045i	−0.849897	−	0.490688i
3.14	−0.0120160	−	0.00321968i	0.761682	−	0.584459i	−1.73192	−	0.999923i	3.38537	+	0.907107i	−0.0110342	+	0.00457050i	−0.628724	+	2.56996i	0.0351840	+	0.0351840i	−0.537890	+	2.00743i	−0.0377581	−	0.0217996i
3.15	0.0492328	+	0.0131919i	−1.37958	+	1.05859i	−1.72980	−	0.998701i	2.44382	+	0.654820i	−0.0818854	+	0.0339181i	0.674922	−	2.55822i	−0.144070	−	0.144070i	0.00617438	−	0.0230431i	0.111678	+	0.0644773i
3.16	0.767199	+	0.205570i	−0.489419	+	0.375544i	−1.18572	−	0.684573i	−1.27877	−	0.342645i	−0.452682	+	0.187507i	−2.38152	+	1.15254i	−1.89221	−	1.89221i	−0.677960	+	2.53018i	−0.910632	−	0.525754i
3.17	0.772348	+	0.206950i	2.10066	−	1.61189i	−1.17836	−	0.680325i	0.633392	+	0.169717i	1.95602	−	0.810211i	2.32510	+	1.26249i	−1.90010	−	1.90010i	1.03812	−	3.87430i	0.454076	+	0.262161i
3.18	0.792178	+	0.212263i	1.39160	−	1.06781i	−1.14956	−	0.663699i	−1.93992	−	0.519800i	1.32905	−	0.550510i	−1.09995	−	2.40626i	−1.92961	−	1.92961i	0.0198671	−	0.0741452i	−1.42643	−	0.823549i
3.19	1.28562	+	0.344480i	−1.94647	+	1.49358i	−0.197909	−	0.114263i	−2.20971	−	0.592091i	−3.01691	+	1.24965i	1.03924	−	2.43310i	−2.09735	−	2.09735i	0.781503	−	2.91661i	−2.63688	−	1.52240i
3.20	1.51317	+	0.405453i	1.09181	−	0.837772i	0.393242	+	0.227039i	4.15678	+	1.11381i	1.99177	−	0.825016i	−1.89643	−	1.84487i	−1.71245	−	1.71245i	−0.286279	+	1.06841i	5.83832	+	3.37076i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.d	odd	6	1	inner
41.e	odd	8	1	inner
287.w	even	24	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	287.2.w.a	✓	208
7.d	odd	6	1	inner	287.2.w.a	✓	208
41.e	odd	8	1	inner	287.2.w.a	✓	208
287.w	even	24	1	inner	287.2.w.a	✓	208

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
287.2.w.a	✓	208	1.a	even	1	1	trivial
287.2.w.a	✓	208	7.d	odd	6	1	inner
287.2.w.a	✓	208	41.e	odd	8	1	inner
287.2.w.a	✓	208	287.w	even	24	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(287, [\chi])\).