Newform orbit 667.2.m.a

• Label: 667.2.m.a
• Level: $667$
• Weight: $2$
• Character orbit: 667.m
• Analytic conductor: $5.326$
• Analytic rank: $0$
• Dimension: $580$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.m (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.32602181482\)
Analytic rank:	\(0\)
Dimension:	\(580\)
Relative dimension:	\(58\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 580 q + 42 q^{4} - 14 q^{5} - 40 q^{6} - 22 q^{7} + 28 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
144.1	−2.54580	−	1.16263i	0.749755	−	2.55343i	3.81966	+	4.40812i	1.79747	−	1.15516i	−4.87741	+	5.62883i	0.569562	−	3.96139i	−3.02210	−	10.2923i	−3.43412	−	2.20697i	−5.91902	+	0.851026i
144.2	−2.51111	−	1.14678i	−0.217225	+	0.739800i	3.68082	+	4.24789i	−3.19853	+	2.05557i	1.39387	−	1.60861i	0.0962455	−	0.669402i	−2.81603	−	9.59051i	2.02364	+	1.30052i	10.3891	−	1.49373i
144.3	−2.48132	−	1.13318i	−0.842284	+	2.86855i	3.56314	+	4.11209i	0.774486	−	0.497732i	5.34057	−	6.16335i	−0.176461	+	1.22731i	−2.64453	−	9.00644i	−4.99540	−	3.21035i	−2.48577	+	0.357400i
144.4	−2.18166	−	0.996331i	0.556006	−	1.89358i	2.45725	+	2.83582i	−0.910707	+	0.585276i	−3.09965	+	3.57719i	−0.300085	+	2.08714i	−1.18406	−	4.03253i	−0.752750	−	0.483763i	2.56998	−	0.369508i
144.5	−2.17561	−	0.993569i	0.00167375	−	0.00570027i	2.43639	+	2.81174i	−0.262814	+	0.168900i	−0.00930505	+	0.0107386i	0.234084	−	1.62809i	−1.15931	−	3.94824i	2.52373	+	1.62190i	0.739596	−	0.106338i
144.6	−2.07058	−	0.945601i	0.343410	−	1.16955i	2.08341	+	2.40438i	2.22541	−	1.43018i	−1.81698	+	2.09691i	−0.319932	+	2.22518i	−0.757665	−	2.58037i	1.27385	+	0.818656i	−5.96025	+	0.856955i
144.7	−2.06913	−	0.944942i	−0.381900	+	1.30063i	2.07868	+	2.39892i	1.42266	−	0.914288i	2.01922	−	2.33031i	0.459303	−	3.19452i	−0.752512	−	2.56282i	0.977964	+	0.628499i	−3.80762	+	0.547453i
144.8	−2.04490	−	0.933876i	0.949127	−	3.23243i	1.99978	+	2.30787i	−1.38377	+	0.889294i	−4.95956	+	5.72364i	−0.177723	+	1.23609i	−0.667394	−	2.27294i	−7.02400	−	4.51405i	3.66016	−	0.526252i
144.9	−1.99987	−	0.913310i	−0.304515	+	1.03708i	1.85562	+	2.14150i	−1.61721	+	1.03932i	1.55617	−	1.79591i	−0.658031	+	4.57671i	−0.516342	−	1.75850i	1.54095	+	0.990307i	4.18342	−	0.601485i
144.10	−1.89057	−	0.863396i	0.546078	−	1.85977i	1.51910	+	1.75313i	−3.48014	+	2.23655i	−2.63812	+	3.04456i	0.478945	−	3.33114i	−0.187216	−	0.637599i	−0.636791	−	0.409241i	8.51049	−	1.22362i
144.11	−1.80723	−	0.825333i	−0.788540	+	2.68552i	1.27518	+	1.47163i	−0.498625	+	0.320447i	3.64152	−	4.20254i	−0.0489859	+	0.340704i	0.0295275	+	0.100561i	−4.06647	−	2.61336i	1.16561	−	0.167589i
144.12	−1.66220	−	0.759101i	0.672795	−	2.29133i	0.876951	+	1.01205i	2.47820	−	1.59264i	−2.85767	+	3.29793i	−0.417854	+	2.90624i	0.340223	+	1.15869i	−2.27378	−	1.46127i	−5.32824	+	0.766085i
144.13	−1.54248	−	0.704427i	−0.706327	+	2.40553i	0.573306	+	0.661630i	2.50374	−	1.60906i	2.78402	−	3.21293i	−0.197489	+	1.37356i	0.537236	+	1.82966i	−2.76392	−	1.77626i	−4.99544	+	0.718235i
144.14	−1.48898	−	0.679994i	−0.410781	+	1.39899i	0.444947	+	0.513496i	−2.75771	+	1.77227i	1.56295	−	1.80374i	0.318439	−	2.21479i	0.608995	+	2.07405i	0.735326	+	0.472566i	5.31131	−	0.763651i
144.15	−1.44351	−	0.659230i	0.294625	−	1.00340i	0.339420	+	0.391712i	0.450432	−	0.289475i	−1.08677	+	1.25420i	0.597006	−	4.15227i	0.662444	+	2.25608i	1.60375	+	1.03067i	−0.841035	+	0.120923i
144.16	−1.24405	−	0.568139i	0.489921	−	1.66852i	−0.0848397	−	0.0979102i	−2.34079	+	1.50433i	−1.55744	+	1.79738i	−0.277740	+	1.93172i	0.820537	+	2.79449i	−0.0201691	−	0.0129619i	3.76673	−	0.541574i
144.17	−1.15704	−	0.528401i	−0.256259	+	0.872739i	−0.250194	−	0.288739i	1.57616	−	1.01293i	0.757658	−	0.874384i	−0.622254	+	4.32787i	0.853632	+	2.90720i	1.82776	+	1.17463i	−2.35891	+	0.339160i
144.18	−1.11723	−	0.510223i	−0.0884349	+	0.301182i	−0.321839	−	0.371422i	2.81111	−	1.80659i	0.252472	−	0.291369i	0.132526	−	0.921742i	0.862123	+	2.93612i	2.44087	+	1.56865i	−4.06243	+	0.584089i
144.19	−1.02135	−	0.466436i	0.271355	−	0.924149i	−0.484125	−	0.558710i	−0.771899	+	0.496069i	−0.708204	+	0.817311i	0.190973	−	1.32825i	0.866528	+	2.95112i	1.74334	+	1.12038i	1.01976	−	0.146620i
144.20	−0.941279	−	0.429868i	−0.504321	+	1.71756i	−0.608501	−	0.702248i	−1.58182	+	1.01657i	1.21303	−	1.39991i	−0.00146717	+	0.0102044i	0.853965	+	2.90834i	−0.171912	−	0.110481i	1.92592	−	0.276906i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.c	even	11	1	inner
29.b	even	2	1	inner
667.m	even	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	667.2.m.a	✓	580
23.c	even	11	1	inner	667.2.m.a	✓	580
29.b	even	2	1	inner	667.2.m.a	✓	580
667.m	even	22	1	inner	667.2.m.a	✓	580

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
667.2.m.a	✓	580	1.a	even	1	1	trivial
667.2.m.a	✓	580	23.c	even	11	1	inner
667.2.m.a	✓	580	29.b	even	2	1	inner
667.2.m.a	✓	580	667.m	even	22	1	inner

Hecke kernels

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