Newform orbit 667.2.q.a

• Label: 667.2.q.a
• Level: $667$
• Weight: $2$
• Character orbit: 667.q
• Analytic conductor: $5.326$
• Analytic rank: $0$
• Dimension: $1160$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.q (of order \(44\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.32602181482\)
Analytic rank:	\(0\)
Dimension:	\(1160\)
Relative dimension:	\(58\) over \(\Q(\zeta_{44})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1160 q - 14 q^{2} - 18 q^{3} - 44 q^{7} - 24 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1	−0.932329	−	2.49967i	0.463672	−	0.253184i	−3.86762	+	3.35131i	0.745243	−	0.478939i	−1.06517	−	0.922977i	−0.395951	−	0.0569291i	7.29999	+	3.98610i	−1.47103	+	2.28897i	−1.89200	−	1.41633i
17.2	−0.920518	−	2.46800i	−2.26086	+	1.23452i	−3.73219	+	3.23396i	3.29930	−	2.12033i	5.12796	+	4.44341i	−4.47405	−	0.643271i	6.79322	+	3.70938i	1.96551	−	3.05840i	−8.27004	−	6.19088i
17.3	−0.910462	−	2.44104i	1.83847	−	1.00388i	−3.61825	+	3.13523i	1.32534	−	0.851744i	−4.12438	−	3.57380i	0.646833	+	0.0930005i	6.37427	+	3.48062i	0.750285	−	1.16747i	−3.28582	−	2.45973i
17.4	−0.909074	−	2.43732i	2.87740	−	1.57118i	−3.60263	+	3.12169i	−2.22688	+	1.43113i	−6.44525	−	5.58484i	−4.20625	−	0.604767i	6.31735	+	3.44953i	4.18892	−	6.51809i	5.51253	+	4.12663i
17.5	−0.878129	−	2.35435i	−2.27220	+	1.24071i	−3.26038	+	2.82513i	−1.46870	+	0.943879i	4.91637	+	4.26005i	1.32961	+	0.191169i	5.10356	+	2.78675i	2.00159	−	3.11454i	3.51194	+	2.62900i
17.6	−0.854257	−	2.29035i	−1.68909	+	0.922316i	−3.00445	+	2.60337i	−0.552252	+	0.354911i	3.55535	+	3.08073i	−0.0323345	−	0.00464899i	4.23828	+	2.31428i	0.380453	−	0.591996i	1.28463	+	0.961666i
17.7	−0.784873	−	2.10433i	−0.154682	+	0.0844630i	−2.30067	+	1.99354i	−2.99567	+	1.92520i	0.299144	+	0.259210i	−4.11529	−	0.591689i	2.05838	+	1.12396i	−1.60513	+	2.49763i	6.40247	+	4.79283i
17.8	−0.750458	−	2.01206i	0.400767	−	0.218835i	−1.97368	+	1.71020i	−0.140927	+	0.0905682i	−0.741068	−	0.642139i	−0.0154010	−	0.00221433i	1.15264	+	0.629391i	−1.50920	+	2.34836i	0.287988	+	0.215585i
17.9	−0.749246	−	2.00881i	2.42681	−	1.32514i	−1.96244	+	1.70046i	3.30998	−	2.12719i	−4.48023	−	3.88214i	3.34368	+	0.480748i	1.12278	+	0.613086i	2.51150	−	3.90796i	−6.75311	−	5.05531i
17.10	−0.738175	−	1.97912i	1.24724	−	0.681045i	−1.86053	+	1.61216i	−2.34841	+	1.50923i	−2.26855	−	1.96571i	3.25839	+	0.468485i	0.856202	+	0.467522i	−0.530136	+	0.824908i	4.72050	+	3.53372i
17.11	−0.675098	−	1.81001i	−0.346162	+	0.189019i	−1.30887	+	1.13414i	3.42496	−	2.20109i	0.575819	+	0.498950i	1.94403	+	0.279509i	−0.454591	−	0.248225i	−1.53782	+	2.39290i	−6.29617	−	4.71326i
17.12	−0.655597	−	1.75772i	−1.43705	+	0.784691i	−1.14829	+	0.994997i	−0.441705	+	0.283866i	2.32140	+	2.01150i	3.82900	+	0.550526i	−0.791320	−	0.432093i	−0.172538	+	0.268475i	0.788539	+	0.590293i
17.13	−0.594527	−	1.59399i	−0.337216	+	0.184134i	−0.675841	+	0.585619i	1.86092	−	1.19594i	0.493991	+	0.428046i	−3.30774	−	0.475582i	−1.65103	−	0.901532i	−1.54211	+	2.39958i	−3.01269	−	2.25527i
17.14	−0.588340	−	1.57740i	2.10725	−	1.15064i	−0.630551	+	0.546375i	1.59578	−	1.02555i	−3.05481	−	2.64700i	−4.02086	−	0.578112i	−1.72240	−	0.940502i	1.49459	−	2.32562i	−2.55656	−	1.91382i
17.15	−0.583599	−	1.56469i	−2.86212	+	1.56284i	−0.596165	+	0.516580i	2.19401	−	1.41000i	4.11568	+	3.56626i	3.16882	+	0.455608i	−1.77521	−	0.969337i	4.12735	−	6.42228i	−3.48663	−	2.61006i
17.16	−0.565894	−	1.51722i	−2.69024	+	1.46898i	−0.470224	+	0.407452i	−2.62071	+	1.68423i	3.75116	+	3.25040i	−4.09228	−	0.588381i	−1.95819	−	1.06925i	3.45756	−	5.38007i	4.03838	+	3.02310i
17.17	−0.553774	−	1.48473i	1.26847	−	0.692638i	−0.386245	+	0.334683i	−2.45133	+	1.57537i	−1.73082	−	1.49977i	−1.32364	−	0.190311i	−2.07080	−	1.13074i	−0.492650	+	0.766578i	3.69648	+	2.76715i
17.18	−0.478637	−	1.28328i	2.34372	−	1.27977i	0.0937951	−	0.0812739i	0.457720	−	0.294159i	−2.76409	−	2.39509i	−0.377359	−	0.0542560i	−2.55338	−	1.39425i	2.23329	−	3.47507i	−0.596568	−	0.446585i
17.19	−0.423597	−	1.13571i	0.449099	−	0.245227i	0.401101	−	0.347556i	0.274220	−	0.176231i	−0.468743	−	0.406168i	4.72713	+	0.679659i	−2.69236	−	1.47014i	−1.48037	+	2.30350i	−0.316305	−	0.236783i
17.20	−0.344879	−	0.924656i	−1.07132	+	0.584985i	0.775452	−	0.671933i	−2.72457	+	1.75097i	0.910385	+	0.788853i	1.73657	+	0.249681i	−2.62107	−	1.43121i	−0.816404	+	1.27035i	2.55870	+	1.91542i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.d	odd	22	1	inner
29.c	odd	4	1	inner
667.q	even	44	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	667.2.q.a	✓	1160
23.d	odd	22	1	inner	667.2.q.a	✓	1160
29.c	odd	4	1	inner	667.2.q.a	✓	1160
667.q	even	44	1	inner	667.2.q.a	✓	1160

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
667.2.q.a	✓	1160	1.a	even	1	1	trivial
667.2.q.a	✓	1160	23.d	odd	22	1	inner
667.2.q.a	✓	1160	29.c	odd	4	1	inner
667.2.q.a	✓	1160	667.q	even	44	1	inner

Hecke kernels

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