Newform orbit 667.2.u.a

• Label: 667.2.u.a
• Level: $667$
• Weight: $2$
• Character orbit: 667.u
• Analytic conductor: $5.326$
• Analytic rank: $0$
• Dimension: $3480$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.u (of order \(154\), degree \(60\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.32602181482\)
Analytic rank:	\(0\)
Dimension:	\(3480\)
Relative dimension:	\(58\) over \(\Q(\zeta_{154})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{154}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 3480 q - 63 q^{2} - 63 q^{3} - 105 q^{4} - 49 q^{5} - 51 q^{6} - 41 q^{7} - 84 q^{8} - 91 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1	−0.549653	−	2.65690i	−0.0369874	−	0.0409665i	−4.92118	+	2.12720i	2.56380	−	2.51202i	−0.0885136	+	0.120789i	2.05343	+	3.05627i	5.23925	+	7.46441i	0.305159	−	2.98138i	−8.08340	−	5.43102i
4.2	−0.545466	−	2.63666i	−1.18274	−	1.30998i	−4.81863	+	2.08287i	−2.00603	+	1.96552i	−2.80884	+	3.83305i	0.697018	+	1.03743i	5.02653	+	7.16134i	−0.0117039	+	0.114346i	6.27664	+	4.21710i
4.3	−0.531054	−	2.56700i	2.03880	+	2.25813i	−4.47163	+	1.93288i	0.250657	−	0.245596i	4.71391	−	6.43278i	−0.956611	−	1.42380i	4.32442	+	6.16103i	−0.636989	+	6.22333i	−0.763556	−	0.513013i
4.4	−0.506463	−	2.44813i	0.669511	+	0.741536i	−3.90102	+	1.68623i	−0.535395	+	0.524583i	1.47630	−	2.01461i	−0.248759	−	0.370247i	3.23135	+	4.60374i	0.203837	−	1.99147i	1.55541	+	1.04504i
4.5	−0.504872	−	2.44044i	1.39688	+	1.54715i	−3.86504	+	1.67068i	−0.360643	+	0.353360i	3.07049	−	4.19011i	2.29928	+	3.42219i	3.16508	+	4.50932i	−0.136946	+	1.33795i	1.04443	+	0.701728i
4.6	−0.479420	−	2.31741i	−1.24775	−	1.38198i	−3.30473	+	1.42848i	1.73083	−	1.69588i	−2.60443	+	3.55410i	−0.993686	−	1.47898i	2.17563	+	3.09964i	−0.0475267	+	0.464332i	−4.75985	−	3.19802i
4.7	−0.454734	−	2.19809i	−0.100075	−	0.110841i	−2.78897	+	1.20555i	−1.97020	+	1.93041i	−0.198130	+	0.270376i	−2.21723	−	3.30007i	1.33904	+	1.90774i	0.303198	−	2.96222i	5.13914	+	3.45285i
4.8	−0.447110	−	2.16123i	−1.40317	−	1.55412i	−2.63519	+	1.13907i	1.38554	−	1.35756i	−2.73145	+	3.72744i	0.422913	+	0.629454i	1.10417	+	1.57312i	−0.140941	+	1.37699i	−3.55349	−	2.38750i
4.9	−0.421556	−	2.03771i	0.434970	+	0.481764i	−2.13873	+	0.924473i	1.81756	−	1.78086i	0.798332	−	1.08943i	−2.41486	−	3.59422i	0.394477	+	0.562014i	0.262571	−	2.56530i	−4.39508	−	2.95294i
4.10	−0.411927	−	1.99116i	−2.15255	−	2.38413i	−1.95921	+	0.846879i	−0.158097	+	0.154904i	−3.86049	+	5.26817i	2.85919	+	4.25555i	0.157018	+	0.223704i	−0.745094	+	7.27951i	0.373563	+	0.250987i
4.11	−0.401211	−	1.93937i	−0.0273517	−	0.0302942i	−1.76434	+	0.762644i	−1.73901	+	1.70390i	−0.0477778	+	0.0651994i	0.953671	+	1.41942i	−0.0886148	−	0.126250i	0.305299	−	2.98275i	4.00219	+	2.68897i
4.12	−0.376225	−	1.81859i	1.56277	+	1.73089i	−1.32988	+	0.574848i	−0.702947	+	0.688752i	2.55982	−	3.49323i	−0.807846	−	1.20238i	−0.588074	−	0.837835i	−0.248267	+	2.42555i	1.51702	+	1.01925i
4.13	−0.369973	−	1.78837i	0.784670	+	0.869084i	−1.22556	+	0.529753i	2.78107	−	2.72491i	1.26394	−	1.72482i	−0.281512	−	0.418995i	−0.697546	−	0.993800i	0.165868	−	1.62052i	−5.90208	−	3.96545i
4.14	−0.346908	−	1.67688i	1.92093	+	2.12758i	−0.855740	+	0.369897i	−2.77227	+	2.71628i	2.90131	−	3.95924i	−0.980485	−	1.45933i	−1.05041	−	1.49653i	−0.531167	+	5.18946i	5.51659	+	3.70645i
4.15	−0.313092	−	1.51342i	−1.02547	−	1.13579i	−0.356581	+	0.154134i	0.299738	−	0.293685i	−1.39786	+	1.90758i	0.0333896	+	0.0496963i	−1.43084	−	2.03853i	0.0670393	−	0.654969i	−0.538315	−	0.361680i
4.16	−0.301495	−	1.45736i	2.05489	+	2.27596i	−0.197172	+	0.0852286i	1.60989	−	1.57738i	2.69735	−	3.68091i	1.68389	+	2.50626i	−1.52632	−	2.17457i	−0.651928	+	6.36928i	−2.78418	−	1.87062i
4.17	−0.281431	−	1.36038i	−0.426723	−	0.472629i	0.0644155	−	0.0278439i	−3.04870	+	2.98713i	−0.522860	+	0.713515i	2.40462	+	3.57898i	−1.65219	−	2.35389i	0.264183	−	2.58104i	4.92162	+	3.30671i
4.18	−0.268126	−	1.29606i	0.851696	+	0.943321i	0.227944	−	0.0985298i	1.04828	−	1.02711i	0.994242	−	1.35678i	1.73800	+	2.58679i	−1.70954	−	2.43560i	0.141000	−	1.37756i	−1.61227	−	1.08324i
4.19	−0.247370	−	1.19573i	−1.53071	−	1.69538i	0.467244	−	0.201968i	−1.17093	+	1.14729i	−1.64858	+	2.24971i	0.0489480	+	0.0728529i	−1.76008	−	2.50761i	−0.225783	+	2.20588i	1.66150	+	1.11632i
4.20	−0.229353	−	1.10864i	−1.27498	−	1.41214i	0.659349	−	0.285006i	−0.878971	+	0.861221i	−1.27314	+	1.73738i	−2.69047	−	4.00443i	−1.76801	−	2.51889i	−0.0631032	+	0.616513i	1.15638	+	0.776941i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.c	even	11	1	inner
29.e	even	14	1	inner
667.u	even	154	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	667.2.u.a	✓	3480
23.c	even	11	1	inner	667.2.u.a	✓	3480
29.e	even	14	1	inner	667.2.u.a	✓	3480
667.u	even	154	1	inner	667.2.u.a	✓	3480

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
667.2.u.a	✓	3480	1.a	even	1	1	trivial
667.2.u.a	✓	3480	23.c	even	11	1	inner
667.2.u.a	✓	3480	29.e	even	14	1	inner
667.2.u.a	✓	3480	667.u	even	154	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(667, [\chi])\).