Newform orbit 483.2.n.a

• Label: 483.2.n.a
• Level: $483$
• Weight: $2$
• Character orbit: 483.n
• Analytic conductor: $3.857$
• Analytic rank: $0$
• Dimension: $116$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.n (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.85677441763\)
Analytic rank:	\(0\)
Dimension:	\(116\)
Relative dimension:	\(58\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 116 q + 56 q^{4} - 10 q^{7} - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
47.1	−2.44467	−	1.41143i	1.69781	−	0.342692i	2.98426	+	5.16889i	0.950213	−	1.64582i	−4.63427	−	1.55857i	−1.23167	−	2.34158i		−	11.2026i	2.76512	−	1.16365i	−4.64591	+	2.68232i
47.2	−2.33544	−	1.34837i	−1.04040	+	1.38476i	2.63619	+	4.56602i	−0.0332776	+	0.0576385i	4.29696	−	1.83120i	−1.58536	+	2.11817i		−	8.82477i	−0.835146	−	2.88141i	0.155436	−	0.0897409i
47.3	−2.29312	−	1.32393i	−1.35264	−	1.08184i	2.50559	+	4.33981i	−2.05000	+	3.55071i	1.66947	+	4.27158i	−0.0386680	−	2.64547i		−	7.97318i	0.659249	+	2.92667i	9.40179	−	5.42813i
47.4	−2.13598	−	1.23321i	−1.67324	+	0.447500i	2.04161	+	3.53618i	1.36168	−	2.35849i	4.12588	+	1.10761i	2.39415	−	1.12607i		−	5.13811i	2.59949	−	1.49755i	−5.81703	+	3.35846i
47.5	−2.09741	−	1.21094i	1.21100	+	1.23833i	1.93276	+	3.34764i	−0.868774	+	1.50476i	−1.04042	−	4.06375i	2.64399	−	0.0966161i		−	4.51808i	−0.0669439	+	2.99925i	3.64436	−	2.10407i
47.6	−2.01952	−	1.16597i	0.890949	+	1.48533i	1.71897	+	2.97735i	1.28353	−	2.22314i	−0.0674375	−	4.03848i	−0.527114	+	2.59271i		−	3.35320i	−1.41242	+	2.64671i	−5.18423	+	2.99312i
47.7	−1.95986	−	1.13153i	−1.38096	−	1.04545i	1.56071	+	2.70323i	0.105593	−	0.182893i	1.52353	+	3.61153i	1.41527	+	2.23540i		−	2.53784i	0.814080	+	2.88743i	−0.413897	+	0.238964i
47.8	−1.94838	−	1.12490i	0.249841	−	1.71394i	1.53079	+	2.65141i	−0.341657	+	0.591768i	−2.41479	+	3.05836i	−2.51638	+	0.817220i		−	2.38836i	−2.87516	−	0.856422i	1.33136	−	0.768660i
47.9	−1.85789	−	1.07265i	−0.419028	+	1.68060i	1.30116	+	2.25367i	−0.826951	+	1.43232i	2.58120	−	2.67289i	−0.559247	−	2.58597i		−	1.29215i	−2.64883	−	1.40844i	3.07276	−	1.77406i
47.10	−1.81419	−	1.04742i	−0.759538	−	1.55663i	1.19418	+	2.06838i	1.94488	−	3.36863i	−0.252504	+	3.61957i	−0.829752	−	2.51227i		−	0.813554i	−1.84620	+	2.36464i	−7.05676	+	4.07422i
47.11	−1.75262	−	1.01188i	1.45057	−	0.946485i	1.04778	+	1.81482i	1.57777	−	2.73277i	−3.50003	+	0.191028i	1.90338	+	1.83770i		−	0.193410i	1.20833	−	2.74589i	−5.53045	+	3.19301i
47.12	−1.61162	−	0.930468i	−1.59984	+	0.663721i	0.731543	+	1.26707i	−2.09187	+	3.62322i	3.19590	+	0.418931i	0.0287355	+	2.64560i			0.999164i	2.11895	−	2.12369i	6.74259	−	3.89284i
47.13	−1.56218	−	0.901925i	1.68751	+	0.390253i	0.626938	+	1.08589i	−0.604515	+	1.04705i	−2.28422	−	2.13166i	−2.35039	−	1.21476i			1.34590i	2.69541	+	1.31711i	1.88872	−	1.09045i
47.14	−1.40944	−	0.813741i	1.19429	−	1.25446i	0.324350	+	0.561790i	−0.349118	+	0.604691i	−2.70409	+	0.796242i	0.554890	−	2.58691i			2.19922i	−0.147336	−	2.99638i	0.984123	−	0.568184i
47.15	−1.33899	−	0.773067i	−1.69734	−	0.345005i	0.195266	+	0.338210i	0.489073	−	0.847100i	2.00602	+	1.77412i	−2.35128	+	1.21304i			2.48845i	2.76194	+	1.17118i	−1.30973	+	0.756173i
47.16	−1.18271	−	0.682837i	−1.09928	+	1.33850i	−0.0674665	−	0.116855i	1.64053	−	2.84148i	2.21410	−	0.832434i	−2.62678	−	0.316234i			2.91562i	−0.583186	−	2.94277i	−3.88054	+	2.24043i
47.17	−1.08140	−	0.624349i	−0.486586	+	1.66230i	−0.220377	−	0.381705i	1.03800	−	1.79786i	1.56405	−	1.49382i	2.55312	+	0.693956i			3.04776i	−2.52647	−	1.61770i	−2.24498	+	1.29614i
47.18	−1.07338	−	0.619715i	−0.722709	−	1.57407i	−0.231907	−	0.401675i	−0.273772	+	0.474187i	−0.199734	+	2.13744i	2.55123	−	0.700882i			3.05372i	−1.95538	+	2.27519i	0.587721	−	0.339321i
47.19	−1.06618	−	0.615560i	0.610600	+	1.62085i	−0.242171	−	0.419452i	−1.71746	+	2.97473i	0.346722	−	2.10399i	−2.51610	+	0.818060i			3.05852i	−2.25433	+	1.97939i	3.66225	−	2.11440i
47.20	−0.995717	−	0.574877i	1.25957	+	1.18890i	−0.339032	−	0.587221i	1.31638	−	2.28004i	−0.570703	−	1.90791i	1.26124	−	2.32579i			3.07912i	0.173032	+	2.99501i	−2.62149	+	1.51352i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
7.d	odd	6	1	inner
21.g	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	483.2.n.a	✓	116
3.b	odd	2	1	inner	483.2.n.a	✓	116
7.d	odd	6	1	inner	483.2.n.a	✓	116
21.g	even	6	1	inner	483.2.n.a	✓	116

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
483.2.n.a	✓	116	1.a	even	1	1	trivial
483.2.n.a	✓	116	3.b	odd	2	1	inner
483.2.n.a	✓	116	7.d	odd	6	1	inner
483.2.n.a	✓	116	21.g	even	6	1	inner

Hecke kernels

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