Newform orbit 143.4.j.a

• Label: 143.4.j.a
• Level: $143$
• Weight: $4$
• Character orbit: 143.j
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $72$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(36\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
23.1	−4.68493	+	2.70485i	−4.52492	−	7.83739i	10.6324	−	18.4159i			14.9789i	42.3979	+	24.4784i	−18.3113	−	10.5720i			71.7586i	−27.4498	+	47.5444i	−40.5158	−	70.1754i
23.2	−4.60341	+	2.65778i	3.48806	+	6.04150i	10.1276	−	17.5415i		−	11.0780i	−32.1139	−	18.5410i	−13.4565	−	7.76914i			65.1431i	−10.8331	+	18.7635i	29.4429	+	50.9966i
23.3	−4.40125	+	2.54106i	0.865871	+	1.49973i	8.91398	−	15.4395i			8.37251i	−7.62183	−	4.40046i	−3.75563	−	2.16832i			49.9469i	12.0005	−	20.7855i	−21.2751	−	36.8495i
23.4	−4.25281	+	2.45536i	−2.48451	−	4.30330i	8.05759	−	13.9562i		−	14.5097i	21.1323	+	12.2007i	21.5060	+	12.4165i			39.8514i	1.15443	−	1.99953i	35.6265	+	61.7070i
23.5	−4.05448	+	2.34086i	−0.806074	−	1.39616i	6.95923	−	12.0537i		−	5.38645i	6.53643	+	3.77381i	−1.17956	−	0.681020i			27.7085i	12.2005	−	21.1319i	12.6089	+	21.8393i
23.6	−3.65232	+	2.10867i	4.62634	+	8.01306i	4.89294	−	8.47483i			13.5656i	−33.7937	−	19.5108i	13.5120	+	7.80115i			7.53168i	−29.3061	+	50.7597i	−28.6052	−	49.5457i
23.7	−3.43971	+	1.98592i	−0.953208	−	1.65100i	3.88775	−	6.73378i			18.9601i	6.55752	+	3.78599i	20.6923	+	11.9467i		−	0.891668i	11.6828	−	20.2352i	−37.6533	−	65.2174i
23.8	−3.05274	+	1.76250i	−3.30496	−	5.72436i	2.21282	−	3.83272i		−	15.7848i	20.1784	+	11.6500i	−30.7733	−	17.7670i		−	12.5996i	−8.34556	+	14.4549i	27.8208	+	48.1870i
23.9	−2.99291	+	1.72796i	2.70873	+	4.69166i	1.97166	−	3.41501i			9.57590i	−16.2140	−	9.36113i	−24.1322	−	13.9328i		−	14.0195i	−1.17444	+	2.03419i	−16.5467	−	28.6598i
23.10	−2.76240	+	1.59487i	−4.96121	−	8.59307i	1.08722	−	1.88313i			1.24067i	27.4097	+	15.8250i	23.6555	+	13.6575i		−	18.5820i	−35.7273	+	61.8814i	−1.97871	−	3.42722i
23.11	−2.65952	+	1.53547i	−2.90866	−	5.03795i	0.715353	−	1.23903i			4.09794i	15.4713	+	8.93234i	−10.5127	−	6.06949i		−	20.1739i	−3.42061	+	5.92468i	−6.29227	−	10.8985i
23.12	−2.21820	+	1.28068i	0.591773	+	1.02498i	−0.719733	+	1.24661i		−	4.85042i	−2.62534	−	1.51574i	5.49965	+	3.17522i		−	24.1778i	12.7996	−	22.1696i	6.21183	+	10.7592i
23.13	−1.40127	+	0.809025i	1.16324	+	2.01478i	−2.69096	+	4.66087i		−	8.11969i	−3.26002	−	1.88217i	−7.84996	−	4.53218i		−	21.6526i	10.7938	−	18.6954i	6.56903	+	11.3779i
23.14	−0.943417	+	0.544682i	−1.41111	−	2.44412i	−3.40664	+	5.90048i			21.6301i	2.66254	+	1.53722i	−24.7951	−	14.3155i		−	16.1371i	9.51752	−	16.4848i	−11.7815	−	20.4062i
23.15	−0.753305	+	0.434921i	4.96974	+	8.60785i	−3.62169	+	6.27295i		−	11.3907i	−7.48747	−	4.32289i	−24.1895	−	13.9658i		−	13.2593i	−35.8967	+	62.1749i	4.95404	+	8.58064i
23.16	−0.737315	+	0.425689i	−2.76813	−	4.79455i	−3.63758	+	6.30047i			7.50257i	4.08197	+	2.35673i	7.20298	+	4.15864i		−	13.0049i	−1.82513	+	3.16122i	−3.19376	−	5.53176i
23.17	−0.586414	+	0.338566i	−2.81095	−	4.86870i	−3.77075	+	6.53112i		−	21.4343i	3.29676	+	1.90338i	9.06253	+	5.23226i		−	10.5236i	−2.30284	+	3.98864i	7.25695	+	12.5694i
23.18	−0.575952	+	0.332526i	1.60738	+	2.78407i	−3.77885	+	6.54517i			10.5229i	−1.85155	−	1.06899i	25.1101	+	14.4973i		−	10.3467i	8.33263	−	14.4325i	−3.49915	−	6.06070i
23.19	−0.204845	+	0.118267i	3.87126	+	6.70523i	−3.97203	+	6.87975i			11.7890i	−1.58602	−	0.915689i	4.94948	+	2.85759i		−	3.77132i	−16.4734	+	28.5327i	−1.39425	−	2.41491i
23.20	0.200845	−	0.115958i	−4.34402	−	7.52406i	−3.97311	+	6.88162i		−	0.297636i	−1.74495	−	1.00745i	−6.82685	−	3.94148i			3.69817i	−24.2410	+	41.9867i	−0.0345132	−	0.0597786i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
13.e	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	143.4.j.a	✓	72
13.e	even	6	1	inner	143.4.j.a	✓	72
13.f	odd	12	1		1859.4.a.l		36
13.f	odd	12	1		1859.4.a.m		36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
143.4.j.a	✓	72	1.a	even	1	1	trivial
143.4.j.a	✓	72	13.e	even	6	1	inner
1859.4.a.l		36	13.f	odd	12	1
1859.4.a.m		36	13.f	odd	12	1

Hecke kernels

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