Newform orbit 576.2.bm.a

• Label: 576.2.bm.a
• Level: $576$
• Weight: $2$
• Character orbit: 576.bm
• 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.bm (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.

\(\operatorname{Tr}(f)(q) = \) \( 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
13.1	−1.41382	−	0.0331870i	−0.374386	+	1.69110i	1.99780	+	0.0938413i	−0.000471804		0.00138989i	0.585439	−	2.37850i	1.11009	−	1.44669i	−2.82142	−	0.198976i	−2.71967	−	1.26625i	0.000713174	−	0.00194940i
13.2	−1.41279	−	0.0635185i	1.66301	−	0.484141i	1.99193	+	0.179476i	0.131392	−	0.387068i	−2.38023	+	0.578356i	−2.81879	+	3.67352i	−2.80277	−	0.380086i	2.53122	−	1.61026i	−0.210215	+	0.538499i
13.3	−1.40857	+	0.126197i	−1.06415	−	1.36659i	1.96815	−	0.355516i	−0.795912	+	2.34468i	1.67140	+	1.79065i	2.79810	−	3.64656i	−2.72741	+	0.749145i	−0.735151	+	2.90853i	0.825206	−	3.40309i
13.4	−1.40823	−	0.129985i	1.52000	+	0.830426i	1.96621	+	0.366096i	1.17841	−	3.47147i	−2.03256	−	1.36700i	0.673012	−	0.877086i	−2.72128	−	0.771123i	1.62079	+	2.52449i	−2.11070	+	4.73545i
13.5	−1.40630	−	0.149384i	−1.38997	+	1.03343i	1.95537	+	0.420158i	−0.631028	+	1.85895i	2.10910	−	1.24568i	0.0625219	−	0.0814801i	−2.68707	−	0.882971i	0.864037	−	2.87288i	1.16511	−	2.51998i
13.6	−1.38632	+	0.279491i	−1.72237	−	0.182914i	1.84377	−	0.774927i	0.355498	−	1.04726i	2.43887	−	0.227808i	−0.746195	+	0.972460i	−2.33947	+	1.58961i	2.93309	+	0.630089i	−0.200134	+	1.55120i
13.7	−1.35456	+	0.406401i	0.757412	−	1.55767i	1.66968	−	1.10099i	−0.620708	+	1.82855i	−0.392925	+	2.41777i	−1.17718	+	1.53413i	−1.81424	+	2.16992i	−1.85265	−	2.35959i	0.0976643	−	2.72914i
13.8	−1.35449	−	0.406653i	0.905946	+	1.47623i	1.66927	+	1.10161i	−1.35493	+	3.99150i	−0.626776	−	2.36794i	0.639597	−	0.833539i	−1.81302	−	2.17093i	−1.35852	+	2.67477i	3.45839	−	4.85544i
13.9	−1.35331	−	0.410562i	−0.328391	−	1.70063i	1.66288	+	1.11123i	0.981205	−	2.89054i	−0.253802	+	2.43631i	0.185279	−	0.241461i	−1.79416	−	2.18655i	−2.78432	+	1.11695i	−2.51461	+	3.50894i
13.10	−1.33912	+	0.454702i	0.902433	−	1.47838i	1.58649	−	1.21780i	0.807782	−	2.37965i	−0.536243	+	2.39007i	2.02026	−	2.63285i	−1.57077	+	2.35217i	−1.37123	−	2.66828i	0.000313823		3.55394i
13.11	−1.32727	+	0.488210i	1.62021	+	0.612310i	1.52330	−	1.29597i	−1.15808	+	3.41160i	−2.44939	−	0.0217003i	−0.367980	+	0.479561i	−1.38913	+	2.46380i	2.25015	+	1.98414i	−0.128487	−	5.09351i
13.12	−1.31640	−	0.516800i	1.64727	−	0.535253i	1.46584	+	1.36063i	−0.299490	+	0.882268i	−2.44509	−	0.146700i	1.60558	−	2.09243i	−1.22646	−	2.54869i	2.42701	−	1.76341i	0.850205	−	1.00664i
13.13	−1.28635	+	0.587628i	−0.713799	+	1.57813i	1.30939	−	1.51179i	1.42869	−	4.20879i	−0.00915756	−	2.44947i	−1.84067	+	2.39881i	−0.795959	+	2.71412i	−1.98098	−	2.25293i	0.635407	+	6.25352i
13.14	−1.27578	−	0.610228i	−1.60869	−	0.641966i	1.25524	+	1.55704i	−1.11222	+	3.27649i	1.66059	+	1.80068i	−2.57039	+	3.34980i	−0.651268	−	2.75243i	2.17576	+	2.06545i	3.41836	−	3.50138i
13.15	−1.27256	−	0.616911i	−1.71120	+	0.267919i	1.23884	+	1.57012i	1.18675	−	3.49605i	2.34290	+	0.714716i	2.38213	−	3.10445i	−0.607882	−	2.76233i	2.85644	−	0.916929i	−3.66696	+	3.71683i
13.16	−1.25673	−	0.648556i	0.0897512	−	1.72972i	1.15875	+	1.63012i	−0.591531	+	1.74259i	−1.23462	+	2.11559i	−0.895036	+	1.16643i	−0.399010	−	2.80014i	−2.98389	−	0.310490i	1.87357	−	1.80633i
13.17	−1.18741	+	0.768145i	0.146556	+	1.72584i	0.819907	−	1.82421i	−0.0104531	+	0.0307939i	−1.49972	−	1.93671i	1.55545	−	2.02711i	0.427690	+	2.79590i	−2.95704	+	0.505864i	−0.0112420	−	0.0445947i
13.18	−1.18500	+	0.771868i	−0.449175	−	1.67279i	0.808438	−	1.82932i	0.169627	−	0.499705i	1.82345	+	1.63555i	−1.57668	+	2.05477i	0.454001	+	2.79175i	−2.59648	+	1.50275i	0.184699	+	0.723078i
13.19	−1.17354	−	0.789181i	0.665269	+	1.59919i	0.754388	+	1.85227i	0.464376	−	1.36801i	0.481332	−	2.40173i	−0.878947	+	1.14547i	0.576471	−	2.76906i	−2.11483	+	2.12779i	−1.62457	+	1.23893i
13.20	−1.16694	−	0.798899i	−1.18950	+	1.25900i	0.723520	+	1.86454i	0.262679	−	0.773826i	2.39390	−	0.518891i	−1.66626	+	2.17151i	0.645274	−	2.75384i	−0.170166	−	2.99517i	−0.924740	+	0.693158i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.c	even	3	1	inner
64.i	even	16	1	inner
576.bm	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.bm.a	✓	1504
9.c	even	3	1	inner	576.2.bm.a	✓	1504
64.i	even	16	1	inner	576.2.bm.a	✓	1504
576.bm	even	48	1	inner	576.2.bm.a	✓	1504

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
576.2.bm.a	✓	1504	1.a	even	1	1	trivial
576.2.bm.a	✓	1504	9.c	even	3	1	inner
576.2.bm.a	✓	1504	64.i	even	16	1	inner
576.2.bm.a	✓	1504	576.bm	even	48	1	inner

Hecke kernels

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