Newform orbit 143.4.w.a

• Label: 143.4.w.a
• Level: $143$
• Weight: $4$
• Character orbit: 143.w
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $640$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.w (of order \(60\), degree \(16\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(640\)
Relative dimension:	\(40\) over \(\Q(\zeta_{60})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 640 q - 20 q^{2} - 6 q^{3} - 18 q^{4} - 12 q^{5} - 20 q^{6} - 20 q^{7} - 20 q^{8} + 642 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−4.61575	−	2.99751i	−0.866584	−	0.385828i	9.06625	+	20.3631i	−16.7403	−	8.52960i	2.84342	+	4.37848i	9.35497	−	24.3705i	12.3033	−	77.6801i	−17.4644	−	19.3962i	51.7015	+	89.5496i
2.2	−4.50283	−	2.92417i	−5.02636	−	2.23788i	8.47080	+	19.0257i	4.12727	+	2.10295i	16.0889	+	24.7747i	−10.6643	+	27.7815i	10.7727	−	68.0164i	2.18964	+	2.43184i	−12.4350	−	21.5381i
2.3	−4.35952	−	2.83111i	5.31423	+	2.36605i	7.73636	+	17.3762i	13.2395	+	6.74586i	−16.4690	−	25.3600i	4.68860	−	12.2142i	8.96156	−	56.5811i	4.57635	+	5.08255i	−38.6196	−	66.8911i
2.4	−4.06520	−	2.63997i	8.74527	+	3.89365i	6.30249	+	14.1556i	−10.6455	−	5.42415i	−25.2721	−	38.9157i	−7.80705	+	20.3381i	5.68342	−	35.8837i	43.2528	+	48.0371i	28.9564	+	50.1540i
2.5	−3.75529	−	2.43872i	−3.69699	−	1.64600i	4.90100	+	11.0078i	8.76581	+	4.46640i	9.86913	+	15.1971i	6.22368	−	16.2132i	2.83656	−	17.9093i	−7.10815	−	7.89440i	−22.0259	−	38.1500i
2.6	−3.73512	−	2.42562i	2.56251	+	1.14090i	4.81363	+	10.8116i	−2.56515	−	1.30701i	−6.80388	−	10.4771i	−4.48558	+	11.6853i	2.67168	−	16.8683i	−12.8017	−	14.2178i	6.41083	+	11.1039i
2.7	−3.61764	−	2.34932i	−8.83031	−	3.93151i	4.31410	+	9.68962i	−6.26308	−	3.19120i	22.7085	+	34.9680i	2.63177	−	6.85599i	1.75890	−	11.1053i	44.4510	+	49.3679i	15.1604	+	26.2586i
2.8	−3.12805	−	2.03138i	5.19148	+	2.31140i	2.40430	+	5.40015i	0.717477	+	0.365573i	−11.5439	−	17.7760i	4.70905	−	12.2675i	−1.21874	+	7.69482i	3.54240	+	3.93424i	−1.50169	−	2.60100i
2.9	−2.96020	−	1.92238i	−4.52412	−	2.01427i	1.81337	+	4.07289i	−3.12928	−	1.59445i	9.52013	+	14.6597i	−1.90673	+	4.96720i	−1.95556	+	12.3469i	−1.65614	−	1.83933i	6.19818	+	10.7356i
2.10	−2.94463	−	1.91226i	1.58522	+	0.705785i	1.76019	+	3.95345i	14.9771	+	7.63121i	−3.31823	−	5.10963i	−8.30045	+	21.6234i	−2.01708	+	12.7353i	−16.0517	−	17.8273i	−29.5091	−	51.1113i
2.11	−2.62944	−	1.70758i	1.89477	+	0.843607i	0.744240	+	1.67159i	−16.7269	−	8.52278i	−3.54166	−	5.45368i	1.54432	−	4.02309i	−3.02625	+	19.1070i	−15.1880	−	16.8680i	29.4291	+	50.9727i
2.12	−2.05191	−	1.33253i	−4.55695	−	2.02888i	−0.819179	−	1.83991i	−15.5428	−	7.91944i	6.64692	+	10.2354i	−9.19210	+	23.9462i	−3.83273	+	24.1989i	−1.41711	−	1.57386i	21.3395	+	36.9612i
2.13	−2.03945	−	1.32443i	−3.45137	−	1.53665i	−0.848666	−	1.90614i	7.68362	+	3.91500i	5.00371	+	7.70503i	11.4289	−	29.7734i	−3.83703	+	24.2261i	−8.51585	−	9.45781i	−10.4852	−	18.1609i
2.14	−1.60685	−	1.04350i	8.46099	+	3.76707i	−1.76082	−	3.95486i	14.7384	+	7.50959i	−9.66460	−	14.8822i	4.46294	−	11.6264i	−3.69530	+	23.3312i	39.3309	+	43.6814i	−15.8462	−	27.4464i
2.15	−1.46478	−	0.951240i	−9.44006	−	4.20299i	−2.01317	−	4.52165i	13.4542	+	6.85525i	9.82957	+	15.1362i	−4.19617	+	10.9314i	−3.53809	+	22.3386i	53.3831	+	59.2880i	−13.1864	−	22.8396i
2.16	−1.41854	−	0.921209i	4.78676	+	2.13120i	−2.09027	−	4.69482i	−6.68912	−	3.40828i	−4.82692	−	7.43280i	7.57564	−	19.7352i	−3.47655	+	21.9501i	0.304533	+	0.338218i	6.34904	+	10.9969i
2.17	−1.28263	−	0.832949i	7.41783	+	3.30263i	−2.30256	−	5.17164i	−1.35664	−	0.691245i	−6.76340	−	10.4147i	−10.4457	+	27.2119i	−3.26833	+	20.6354i	26.0503	+	28.9318i	1.16430	+	2.01662i
2.18	−1.26284	−	0.820099i	−2.99685	−	1.33428i	−2.33169	−	5.23705i	14.0544	+	7.16106i	2.69030	+	4.14269i	−4.84976	+	12.6340i	−3.23478	+	20.4236i	−10.8658	−	12.0676i	−11.8757	−	20.5692i
2.19	−0.293417	−	0.190547i	0.878279	+	0.391035i	−3.20411	−	7.19654i	0.705520	+	0.359480i	−0.183191	−	0.282090i	−6.01679	+	15.6743i	−0.868983	+	5.48654i	−17.4481	−	19.3780i	−0.138514	−	0.239913i
2.20	−0.257450	−	0.167190i	−4.17549	−	1.85905i	−3.21557	−	7.22228i	−8.58006	−	4.37176i	0.764164	+	1.17671i	1.42206	−	3.70460i	−0.763815	+	4.82254i	−4.08788	−	4.54005i	1.47802	+	2.56000i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.d	odd	10	1	inner
13.f	odd	12	1	inner
143.w	even	60	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	143.4.w.a	✓	640
11.d	odd	10	1	inner	143.4.w.a	✓	640
13.f	odd	12	1	inner	143.4.w.a	✓	640
143.w	even	60	1	inner	143.4.w.a	✓	640

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
143.4.w.a	✓	640	1.a	even	1	1	trivial
143.4.w.a	✓	640	11.d	odd	10	1	inner
143.4.w.a	✓	640	13.f	odd	12	1	inner
143.4.w.a	✓	640	143.w	even	60	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(143, [\chi])\).