Newform orbit 572.2.t.a

• Label: 572.2.t.a
• Level: $572$
• Weight: $2$
• Character orbit: 572.t
• Analytic conductor: $4.567$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.56744299562\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(80\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 160 q - 2 q^{4} - 16 q^{5} + 68 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
87.1	−1.41020	+	0.106478i	0.151443	+	0.0874355i	1.97732	−	0.300310i	−4.25810			−0.222875	−	0.107176i	1.66734	+	2.88791i	−2.75645	+	0.634039i	−1.48471	−	2.57159i	6.00478	−	0.453394i
87.2	−1.40800	−	0.132444i	1.78274	+	1.02926i	1.96492	+	0.372961i	1.58498			−2.37377	−	1.68531i	1.72331	+	2.98486i	−2.71720	−	0.785368i	0.618768	+	1.07174i	−2.23164	−	0.209920i
87.3	−1.39957	−	0.203000i	−2.41412	−	1.39379i	1.91758	+	0.568224i	2.71349			3.09579	+	2.44077i	−1.13343	−	1.96316i	−2.56844	−	1.18454i	2.38532	+	4.13149i	−3.79771	−	0.550837i
87.4	−1.39945	−	0.203823i	−0.783384	−	0.452287i	1.91691	+	0.570480i	2.92431			1.00412	+	0.792624i	−0.351276	−	0.608428i	−2.56634	−	1.18907i	−1.09087	−	1.88945i	−4.09242	−	0.596043i
87.5	−1.39552	+	0.229204i	2.08234	+	1.20224i	1.89493	−	0.639716i	−2.36335			−3.18150	−	1.20047i	−1.42248	−	2.46380i	−2.49778	+	1.32706i	1.39077	+	2.40888i	3.29809	−	0.541689i
87.6	−1.36138	+	0.382925i	−1.69448	−	0.978307i	1.70674	−	1.04262i	−1.87383			2.68146	+	0.682994i	0.639155	+	1.10705i	−1.92428	+	2.07296i	0.414171	+	0.717364i	2.55100	−	0.717536i
87.7	−1.35748	+	0.396562i	−0.410459	−	0.236978i	1.68548	−	1.07664i	−1.00051			0.651164	+	0.158920i	−1.25701	−	2.17721i	−1.86104	+	2.12991i	−1.38768	−	2.40354i	1.35817	−	0.396764i
87.8	−1.35030	−	0.420348i	−2.86468	−	1.65392i	1.64661	+	1.13519i	−3.67952			3.17295	+	3.43745i	−0.939669	−	1.62756i	−1.74625	−	2.22500i	3.97092	+	6.87783i	4.96846	+	1.54668i
87.9	−1.34933	−	0.423444i	1.94116	+	1.12073i	1.64139	+	1.14273i	−0.245835			−2.14470	−	2.33421i	−0.228705	−	0.396129i	−1.73089	−	2.23696i	1.01207	+	1.75295i	0.331712	+	0.104097i
87.10	−1.33912	+	0.454709i	0.665321	+	0.384123i	1.58648	−	1.21782i	2.62826			−1.06561	−	0.211859i	−0.983531	−	1.70353i	−1.57073	+	2.35219i	−1.20490	−	2.08695i	−3.51955	+	1.19509i
87.11	−1.33705	−	0.460748i	−0.847243	−	0.489156i	1.57542	+	1.23209i	1.08222			0.907431	+	1.04439i	2.37503	+	4.11368i	−1.53874	−	2.37324i	−1.02145	−	1.76921i	−1.44699	−	0.498633i
87.12	−1.30161	−	0.552996i	0.965312	+	0.557323i	1.38839	+	1.43957i	−1.84918			−0.948265	−	1.25923i	−0.798405	−	1.38288i	−1.01107	−	2.64154i	−0.878782	−	1.52209i	2.40691	+	1.02259i
87.13	−1.20939	+	0.733056i	2.20753	+	1.27452i	0.925257	−	1.77310i	−0.492373			−3.60406	+	0.0768518i	2.32336	+	4.02417i	0.180786	+	2.82264i	1.74880	+	3.02900i	0.595472	−	0.360937i
87.14	−1.19068	+	0.763078i	−2.37620	−	1.37190i	0.835423	−	1.81716i	1.57679			3.87615	−	0.179738i	0.286729	+	0.496630i	0.391917	+	2.80114i	2.26422	+	3.92174i	−1.87745	+	1.20322i
87.15	−1.12971	−	0.850732i	−0.965312	−	0.557323i	0.552511	+	1.92217i	−1.84918			0.616395	+	1.45084i	0.798405	+	1.38288i	1.01107	−	2.64154i	−0.878782	−	1.52209i	2.08904	+	1.57315i
87.16	−1.06755	−	0.927548i	0.847243	+	0.489156i	0.279310	+	1.98040i	1.08222			−0.450755	−	1.30805i	−2.37503	−	4.11368i	1.53874	−	2.37324i	−1.02145	−	1.76921i	−1.15532	−	1.00382i
87.17	−1.05336	+	0.943626i	−1.81974	−	1.05063i	0.219139	−	1.98796i	−2.74224			2.90824	−	0.610464i	−2.27804	−	3.94569i	1.64506	+	2.30082i	0.707629	+	1.22565i	2.88857	−	2.58765i
87.18	−1.04138	−	0.956833i	−1.94116	−	1.12073i	0.168941	+	1.99285i	−0.245835			0.949133	+	3.02447i	0.228705	+	0.396129i	1.73089	−	2.23696i	1.01207	+	1.75295i	0.256007	+	0.235223i
87.19	−1.03918	−	0.959219i	2.86468	+	1.65392i	0.159798	+	1.99361i	−3.67952			−1.39045	−	4.46658i	0.939669	+	1.62756i	1.74625	−	2.22500i	3.97092	+	6.87783i	3.82369	+	3.52947i
87.20	−1.00532	+	0.994647i	2.84151	+	1.64055i	0.0213531	−	1.99989i	0.805960			−4.48841	+	1.17702i	−0.565511	−	0.979494i	1.96771	+	2.03177i	3.88279	+	6.72520i	−0.810251	+	0.801646i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
11.b	odd	2	1	inner
13.c	even	3	1	inner
44.c	even	2	1	inner
52.j	odd	6	1	inner
143.k	odd	6	1	inner
572.t	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	572.2.t.a	✓	160
4.b	odd	2	1	inner	572.2.t.a	✓	160
11.b	odd	2	1	inner	572.2.t.a	✓	160
13.c	even	3	1	inner	572.2.t.a	✓	160
44.c	even	2	1	inner	572.2.t.a	✓	160
52.j	odd	6	1	inner	572.2.t.a	✓	160
143.k	odd	6	1	inner	572.2.t.a	✓	160
572.t	even	6	1	inner	572.2.t.a	✓	160

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
572.2.t.a	✓	160	1.a	even	1	1	trivial
572.2.t.a	✓	160	4.b	odd	2	1	inner
572.2.t.a	✓	160	11.b	odd	2	1	inner
572.2.t.a	✓	160	13.c	even	3	1	inner
572.2.t.a	✓	160	44.c	even	2	1	inner
572.2.t.a	✓	160	52.j	odd	6	1	inner
572.2.t.a	✓	160	143.k	odd	6	1	inner
572.2.t.a	✓	160	572.t	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(572, [\chi])\).