Newform orbit 576.2.bl.a

• Label: 576.2.bl.a
• Level: $576$
• Weight: $2$
• Character orbit: 576.bl
• Analytic conductor: $4.599$
• Analytic rank: $0$
• Dimension: $1504$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bl (of order \(48\), degree \(16\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.59938315643\)
Analytic rank:	\(0\)
Dimension:	\(1504\)
Relative dimension:	\(94\) over \(\Q(\zeta_{48})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1504 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−1.41417	+	0.0110611i	1.36345	−	1.06817i	1.99976	−	0.0312846i	2.78390	+	1.37287i	−1.91634	+	1.52566i	0.492179	+	0.641420i	−2.82765	+	0.0663612i	0.718010	−	2.91281i	−3.95209	−	1.91067i
11.2	−1.41165	+	0.0851593i	−1.66601	−	0.473724i	1.98550	−	0.240430i	−1.72799	−	0.852148i	2.39216	+	0.526855i	0.749706	+	0.977036i	−2.78234	+	0.508485i	2.55117	+	1.57846i	2.51187	+	1.05578i
11.3	−1.40351	−	0.173668i	−0.728794	+	1.57126i	1.93968	+	0.487489i	−1.79173	−	0.883583i	1.29575	−	2.07871i	−0.0778075	−	0.101401i	−2.63770	−	1.02106i	−1.93772	−	2.29025i	2.36126	+	1.55128i
11.4	−1.40127	−	0.190903i	−0.555798	−	1.64045i	1.92711	+	0.535013i	−0.879249	−	0.433598i	0.465655	+	2.40482i	−3.05138	−	3.97664i	−2.59827	−	1.11759i	−2.38218	+	1.82352i	1.14929	+	0.775439i
11.5	−1.38867	−	0.267570i	−1.55208	+	0.768797i	1.85681	+	0.743133i	2.74800	+	1.35516i	2.36103	−	0.652317i	−1.12886	−	1.47116i	−2.37966	−	1.52879i	1.81790	−	2.38647i	−3.45347	−	2.61716i
11.6	−1.38521	−	0.284957i	0.799756	+	1.53636i	1.83760	+	0.789449i	1.54938	+	0.764070i	−0.670032	−	2.35607i	2.14122	+	2.79049i	−2.32050	−	1.61719i	−1.72078	+	2.45742i	−1.92849	−	1.49990i
11.7	−1.37786	+	0.318576i	−0.139389	−	1.72643i	1.79702	−	0.877909i	−0.245576	−	0.121104i	0.742059	+	2.33438i	0.961138	+	1.25258i	−2.19637	+	1.78213i	−2.96114	+	0.481292i	0.376951	+	0.0886311i
11.8	−1.36414	−	0.372980i	1.49848	+	0.868647i	1.72177	+	1.01760i	−3.68730	−	1.81838i	−1.72016	−	1.74386i	0.0571406	+	0.0744670i	−1.96920	−	2.03033i	1.49090	+	2.60331i	4.35179	+	3.85582i
11.9	−1.35939	+	0.389931i	1.72496	+	0.156592i	1.69591	−	1.06014i	1.33127	+	0.656508i	−2.40596	+	0.459744i	−1.06088	−	1.38257i	−1.89203	+	2.10244i	2.95096	+	0.540229i	−2.06571	−	0.373352i
11.10	−1.35284	+	0.412086i	−0.492104	+	1.66067i	1.66037	−	1.11497i	1.67682	+	0.826917i	−0.0186000	−	2.44942i	−0.0289848	−	0.0377738i	−1.78676	+	2.19260i	−2.51567	−	1.63445i	−2.60924	−	0.427695i
11.11	−1.34003	+	0.452023i	0.961303	+	1.44080i	1.59135	−	1.21145i	−1.07061	−	0.527968i	−1.93945	−	1.49618i	−2.72460	−	3.55077i	−1.58485	+	2.34270i	−1.15179	+	2.77009i	1.67331	+	0.223550i
11.12	−1.30367	−	0.548138i	1.29483	−	1.15039i	1.39909	+	1.42918i	−1.03041	−	0.508143i	−2.31860	+	0.789982i	1.75332	+	2.28498i	−1.04056	−	2.63006i	0.353186	−	2.97914i	1.06478	+	1.22726i
11.13	−1.28421	+	0.592280i	−1.57042	−	0.730613i	1.29841	−	1.52123i	3.02548	+	1.49200i	2.44948	+	0.00813819i	−2.08079	−	2.71174i	−0.766443	+	2.72260i	1.93241	+	2.29473i	−4.76905	−	0.124119i
11.14	−1.26628	+	0.629706i	1.72410	+	0.165818i	1.20694	−	1.59477i	−1.13197	−	0.558226i	−2.28761	+	0.875702i	3.03857	+	3.95994i	−0.524089	+	2.77945i	2.94501	+	0.571771i	1.78491	−	0.00593726i
11.15	−1.24238	−	0.675648i	1.24724	−	1.20182i	1.08700	+	1.67882i	−0.558818	−	0.275579i	−2.36156	+	0.650421i	−2.33627	−	3.04469i	−0.216171	−	2.82015i	0.111234	−	2.99794i	0.508068	+	0.719937i
11.16	−1.24017	−	0.679688i	−0.405173	−	1.68399i	1.07605	+	1.68586i	3.53047	+	1.74104i	−0.642106	+	2.36383i	0.212417	+	0.276827i	−0.188628	−	2.82213i	−2.67167	+	1.36462i	−3.19503	−	4.55880i
11.17	−1.21036	−	0.731448i	−1.70840	−	0.285283i	0.929967	+	1.77064i	1.45581	+	0.717926i	1.85911	+	1.59490i	2.68057	+	3.49338i	0.169531	−	2.82334i	2.83723	+	0.974751i	−1.23693	−	1.93380i
11.18	−1.18516	−	0.771613i	−0.450297	−	1.67249i	0.809226	+	1.82898i	−3.24873	−	1.60210i	−0.756842	+	2.32963i	1.96855	+	2.56546i	0.452197	−	2.79205i	−2.59447	+	1.50624i	2.61408	+	4.40551i
11.19	−1.14192	+	0.834271i	−1.59577	+	0.673430i	0.607985	−	1.90535i	−1.78193	−	0.878751i	1.26043	−	2.10031i	−0.225755	−	0.294210i	0.895304	+	2.68299i	2.09299	−	2.14928i	2.76795	−	0.483145i
11.20	−1.11718	−	0.867123i	1.58760	+	0.692470i	0.496195	+	1.93747i	0.901826	+	0.444731i	−1.17319	−	2.15026i	−0.914237	−	1.19146i	1.12569	−	2.59477i	2.04097	+	2.19873i	−0.621867	−	1.27884i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.d	odd	6	1	inner
64.j	odd	16	1	inner
576.bl	even	48	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	576.2.bl.a	✓	1504
9.d	odd	6	1	inner	576.2.bl.a	✓	1504
64.j	odd	16	1	inner	576.2.bl.a	✓	1504
576.bl	even	48	1	inner	576.2.bl.a	✓	1504

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
576.2.bl.a	✓	1504	1.a	even	1	1	trivial
576.2.bl.a	✓	1504	9.d	odd	6	1	inner
576.2.bl.a	✓	1504	64.j	odd	16	1	inner
576.2.bl.a	✓	1504	576.bl	even	48	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(576, [\chi])\).