Newform orbit 671.2.q.a

• Label: 671.2.q.a
• Level: $671$
• Weight: $2$
• Character orbit: 671.q
• Analytic conductor: $5.358$
• Analytic rank: $0$
• Dimension: $240$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.q (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.35796197563\)
Analytic rank:	\(0\)
Dimension:	\(240\)
Relative dimension:	\(60\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 240 q - q^{3} - 238 q^{4} - 5 q^{6} - 5 q^{7} - 57 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
113.1		−	2.81541i	−0.0696087	+	0.214233i	−5.92652			−0.582369	+	1.79235i	0.603155	+	0.195977i	1.87318	−	0.608633i			11.0548i	2.38600	+	1.73353i	5.04619	+	1.63961i
113.2		−	2.73694i	0.918399	−	2.82654i	−5.49082			0.523034	−	1.60973i	−7.73606	−	2.51360i	0.369069	−	0.119918i			9.55415i	−4.71882	−	3.42842i	−4.40574	−	1.43151i
113.3		−	2.51417i	−0.257555	+	0.792674i	−4.32103			0.169964	−	0.523095i	1.99291	+	0.647537i	−2.26811	+	0.736953i			5.83546i	1.86505	+	1.35504i	−1.31515	−	0.427317i
113.4		−	2.48160i	−0.482004	+	1.48345i	−4.15833			1.30705	−	4.02268i	3.68134	+	1.19614i	0.765090	−	0.248593i			5.35612i	0.458740	+	0.333294i	−9.98269	−	3.24357i
113.5		−	2.43148i	0.752617	−	2.31632i	−3.91208			−1.24710	+	3.83818i	−5.63207	−	1.82997i	−1.03415	+	0.336016i			4.64918i	−2.37184	−	1.72324i	9.33246	+	3.03230i
113.6		−	2.35298i	0.315173	−	0.970004i	−3.53651			−0.0761250	+	0.234289i	−2.28240	−	0.741596i	−3.79938	+	1.23449i			3.61538i	1.58548	+	1.15192i	0.551276	+	0.179121i
113.7		−	2.32472i	−0.987513	+	3.03925i	−3.40433			0.0585440	−	0.180180i	7.06542	+	2.29569i	3.88869	−	1.26351i			3.26468i	−5.83483	−	4.23925i	−0.418868	−	0.136099i
113.8		−	2.22414i	0.332143	−	1.02223i	−2.94679			−0.483915	+	1.48934i	−2.27358	−	0.738732i	3.77445	−	1.22639i			2.10579i	1.49241	+	1.08430i	3.31249	+	1.07629i
113.9		−	2.17250i	0.601138	−	1.85011i	−2.71976			0.862882	−	2.65568i	−4.01938	−	1.30597i	1.35072	−	0.438875i			1.56368i	−0.634503	−	0.460994i	−5.76947	−	1.87461i
113.10		−	2.02851i	−0.477127	+	1.46845i	−2.11486			−0.990651	+	3.04891i	2.97876	+	0.967858i	2.46627	−	0.801339i			0.232985i	0.498365	+	0.362083i	6.18475	+	2.00955i
113.11		−	1.93074i	0.408463	−	1.25712i	−1.72777			0.916987	−	2.82220i	−2.42717	−	0.788636i	−0.562884	+	0.182892i		−	0.525614i	1.01354	+	0.736383i	−5.44894	−	1.77047i
113.12		−	1.88754i	−0.681683	+	2.09800i	−1.56280			−0.717363	+	2.20782i	3.96006	+	1.28670i	−2.93812	+	0.954653i		−	0.825238i	−1.50988	−	1.09699i	4.16733	+	1.35405i
113.13		−	1.82204i	0.149750	−	0.460883i	−1.31985			−0.214596	+	0.660460i	−0.839750	−	0.272851i	2.48544	−	0.807569i		−	1.23927i	2.23706	+	1.62532i	1.20339	+	0.391004i
113.14		−	1.60793i	−0.695595	+	2.14082i	−0.585438			1.14109	−	3.51193i	3.44229	+	1.11847i	−3.83898	+	1.24736i		−	2.27452i	−1.67221	−	1.21493i	−5.64693	−	1.83480i
113.15		−	1.58170i	−0.879974	+	2.70828i	−0.501773			0.118487	−	0.364664i	4.28369	+	1.39185i	−0.728493	+	0.236702i		−	2.36975i	−4.13338	−	3.00308i	−0.576789	−	0.187410i
113.16		−	1.57351i	0.990113	−	3.04725i	−0.475930			0.243374	−	0.749029i	−4.79488	−	1.55795i	−4.09955	+	1.33202i		−	2.39814i	−5.87838	−	4.27090i	−1.17860	−	0.382952i
113.17		−	1.38154i	0.833936	−	2.56659i	0.0913426			−0.912273	+	2.80769i	−3.54585	−	1.15212i	−0.343729	+	0.111684i		−	2.88928i	−3.46489	−	2.51739i	3.87894	+	1.26034i
113.18		−	1.35927i	−0.165527	+	0.509440i	0.152384			−0.363951	+	1.12013i	0.692466	+	0.224996i	−1.63903	+	0.532554i		−	2.92567i	2.19492	+	1.59470i	1.52255	+	0.494707i
113.19		−	1.14823i	−0.338696	+	1.04240i	0.681569			0.908891	−	2.79728i	1.19691	+	0.388901i	3.70673	−	1.20439i		−	3.07906i	1.45517	+	1.05724i	−3.21192	−	1.04362i
113.20		−	1.08240i	−0.355414	+	1.09385i	0.828409			0.456004	−	1.40343i	1.18399	+	0.384700i	2.92737	−	0.951160i		−	3.06147i	1.35686	+	0.985815i	−1.51908	−	0.493579i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
671.q	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	671.2.q.a	✓	240
11.c	even	5	1		671.2.ba.a	yes	240
61.g	even	10	1		671.2.ba.a	yes	240
671.q	even	10	1	inner	671.2.q.a	✓	240

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
671.2.q.a	✓	240	1.a	even	1	1	trivial
671.2.q.a	✓	240	671.q	even	10	1	inner
671.2.ba.a	yes	240	11.c	even	5	1
671.2.ba.a	yes	240	61.g	even	10	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(671, [\chi])\).