Newform orbit 483.2.bc.a

• Label: 483.2.bc.a
• Level: $483$
• Weight: $2$
• Character orbit: 483.bc
• Analytic conductor: $3.857$
• Analytic rank: $0$
• Dimension: $1200$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bc (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.85677441763\)
Analytic rank:	\(0\)
Dimension:	\(1200\)
Relative dimension:	\(60\) over \(\Q(\zeta_{66})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1200 q - 9 q^{3} - 74 q^{4} - 20 q^{6} - 44 q^{7} - 13 q^{9}+O(q^{10}) \)

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	−1.22080	+	2.36802i	1.28284	−	1.16376i	−2.95705	−	4.15260i	−2.00169	−	1.90861i	1.18972	+	4.45849i	1.48870	+	2.18719i	8.16926	−	1.17456i	0.291334	−	2.98582i	6.96327	−	2.41001i
11.2	−1.21990	+	2.36628i	0.543753	+	1.64449i	−2.95102	−	4.14413i	1.29182	+	1.23174i	−4.55465	−	0.719442i	−2.63893	−	0.189827i	8.13588	−	1.16976i	−2.40867	+	1.78839i	−4.49055	+	1.55419i
11.3	−1.20831	+	2.34379i	−1.45411	+	0.941049i	−2.87322	−	4.03487i	0.0368505	+	0.0351369i	−0.448612	−	4.54519i	0.406340	+	2.61436i	7.70844	−	1.10831i	1.22885	−	2.73677i	−0.126880	+	0.0439136i
11.4	−1.14211	+	2.21537i	1.18000	+	1.26791i	−2.44337	−	3.43123i	−2.09226	−	1.99497i	−4.15658	+	1.16606i	2.18985	−	1.48478i	5.45789	−	0.784726i	−0.215184	+	2.99227i	6.80917	−	2.35668i
11.5	−1.13087	+	2.19357i	−1.61171	+	0.634352i	−2.37279	−	3.33212i	−2.21831	−	2.11515i	0.431125	−	4.25276i	0.0462933	−	2.64535i	5.10697	−	0.734272i	2.19519	−	2.04478i	7.14835	−	2.47407i
11.6	−1.11786	+	2.16834i	1.70544	−	0.302424i	−2.29198	−	3.21863i	1.96583	+	1.87442i	−1.25068	+	4.03605i	1.12495	−	2.39468i	4.71179	−	0.677453i	2.81708	−	1.03153i	−6.26189	+	2.16726i
11.7	−1.07488	+	2.08498i	0.382326	−	1.68933i	−2.03164	−	2.85304i	2.47963	+	2.36432i	3.11125	+	2.61296i	−0.426197	+	2.61120i	3.48857	−	0.501581i	−2.70765	−	1.29175i	−7.59486	+	2.62861i
11.8	−1.02175	+	1.98192i	−1.59600	−	0.672881i	−1.72392	−	2.42090i	1.12079	+	1.06868i	2.96432	−	2.47564i	−2.59123	+	0.534343i	2.14526	−	0.308441i	2.09446	+	2.14784i	−3.26320	+	1.12941i
11.9	−0.970052	+	1.88164i	−0.673848	+	1.59560i	−1.43945	−	2.02142i	2.06335	+	1.96740i	−2.34867	−	2.81575i	2.64569	−	0.0181926i	1.00908	−	0.145084i	−2.09186	−	2.15038i	−5.70349	+	1.97400i
11.10	−0.918620	+	1.78187i	−1.09876	−	1.33893i	−1.17110	−	1.64458i	−2.94599	−	2.80900i	3.39514	−	0.727879i	−1.97640	+	1.75893i	0.0375805	−	0.00540327i	−0.585467	+	2.94232i	7.71152	−	2.66898i
11.11	−0.877897	+	1.70288i	−0.523928	−	1.65091i	−0.968993	−	1.36076i	−0.190109	−	0.181269i	3.27126	+	0.557140i	2.56678	−	0.641583i	−0.624824	+	0.0898362i	−2.45100	+	1.72991i	0.475576	−	0.164598i
11.12	−0.839802	+	1.62899i	0.824775	−	1.52307i	−0.788222	−	1.10690i	−0.179075	−	0.170747i	1.78842	+	2.62263i	−1.48519	−	2.18957i	−1.16305	+	0.167222i	−1.63949	−	2.51238i	0.428532	−	0.148317i
11.13	−0.839508	+	1.62842i	1.58694	+	0.693981i	−0.786858	−	1.10499i	−1.28009	−	1.22056i	−2.46234	+	2.00161i	−1.82028	+	1.92005i	−1.16691	+	0.167776i	2.03678	+	2.20262i	3.06224	−	1.05985i
11.14	−0.823961	+	1.59826i	1.52148	+	0.827710i	−0.715414	−	1.00466i	1.91038	+	1.82155i	−2.57654	+	1.74972i	1.62874	+	2.08499i	−1.36452	+	0.196188i	1.62979	+	2.51868i	−4.48539	+	1.55241i
11.15	−0.745161	+	1.44541i	−1.73201	−	0.0112995i	−0.373834	−	0.524976i	1.43978	+	1.37282i	1.30696	−	2.49505i	0.470528	−	2.60358i	−2.18189	+	0.313709i	2.99974	+	0.0391417i	−3.05716	+	1.05809i
11.16	−0.742085	+	1.43944i	−0.310505	+	1.70399i	−0.361196	−	0.507229i	−1.42767	−	1.36128i	−2.22238	−	1.71146i	−2.18159	−	1.49689i	−2.20781	+	0.317435i	−2.80717	−	1.05820i	3.01893	−	1.04486i
11.17	−0.583726	+	1.13227i	1.30843	−	1.13490i	0.218812	+	0.307278i	−1.12328	−	1.07105i	0.521253	+	2.14397i	2.07224	+	1.64494i	−2.99748	+	0.430973i	0.423986	−	2.96989i	1.86841	−	0.646663i
11.18	−0.571670	+	1.10889i	−1.29954	+	1.14507i	0.257294	+	0.361318i	−1.77881	−	1.69609i	−0.526840	−	2.09565i	0.0113481	+	2.64573i	−3.01749	+	0.433850i	0.377631	−	2.97614i	2.89767	−	1.00289i
11.19	−0.528482	+	1.02511i	−1.73132	−	0.0502508i	0.388554	+	0.545647i	−0.207815	−	0.198151i	0.966484	−	1.74824i	2.41072	+	1.09014i	−3.04785	+	0.438215i	2.99495	+	0.174001i	0.312954	−	0.108314i
11.20	−0.522802	+	1.01409i	−1.07403	+	1.35885i	0.405048	+	0.568811i	2.77635	+	2.64725i	−0.816498	−	1.79957i	−2.48243	+	0.915168i	−3.04721	+	0.438123i	−0.692939	−	2.91888i	−4.13604	+	1.43150i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
7.c	even	3	1	inner
21.h	odd	6	1	inner
23.d	odd	22	1	inner
69.g	even	22	1	inner
161.p	odd	66	1	inner
483.bc	even	66	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	483.2.bc.a	✓	1200
3.b	odd	2	1	inner	483.2.bc.a	✓	1200
7.c	even	3	1	inner	483.2.bc.a	✓	1200
21.h	odd	6	1	inner	483.2.bc.a	✓	1200
23.d	odd	22	1	inner	483.2.bc.a	✓	1200
69.g	even	22	1	inner	483.2.bc.a	✓	1200
161.p	odd	66	1	inner	483.2.bc.a	✓	1200
483.bc	even	66	1	inner	483.2.bc.a	✓	1200

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
483.2.bc.a	✓	1200	1.a	even	1	1	trivial
483.2.bc.a	✓	1200	3.b	odd	2	1	inner
483.2.bc.a	✓	1200	7.c	even	3	1	inner
483.2.bc.a	✓	1200	21.h	odd	6	1	inner
483.2.bc.a	✓	1200	23.d	odd	22	1	inner
483.2.bc.a	✓	1200	69.g	even	22	1	inner
483.2.bc.a	✓	1200	161.p	odd	66	1	inner
483.2.bc.a	✓	1200	483.bc	even	66	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(483, [\chi])\).