Newform orbit 480.2.cb.a

• Label: 480.2.cb.a
• Level: $480$
• Weight: $2$
• Character orbit: 480.cb
• Analytic conductor: $3.833$
• Analytic rank: $0$
• Dimension: $368$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	480.cb (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.83281929702\)
Analytic rank:	\(0\)
Dimension:	\(368\)
Relative dimension:	\(92\) over \(\Q(\zeta_{8})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 368 q - 4 q^{3} - 8 q^{6} - 16 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
53.1	−1.41408	+	0.0197737i	1.09428	+	1.34259i	1.99922	−	0.0559230i	0.580329	−	2.15945i	−1.57394	−	1.87689i	−2.53848			−2.82594	+	0.118611i	−0.605114	+	2.93834i	−0.777928	+	3.06510i
53.2	−1.41387	+	0.0312110i	0.00798375	+	1.73203i	1.99805	−	0.0882566i	1.41029	+	1.73525i	−0.0653464	−	2.44862i	−1.10897			−2.82223	+	0.187144i	−2.99987	+	0.0276562i	−2.04812	−	2.40940i
53.3	−1.41057	−	0.101519i	1.66453	−	0.478907i	1.97939	+	0.286397i	−2.15280	+	0.604538i	−2.39654	+	0.506549i	−3.48201			−2.76298	−	0.604927i	2.54130	−	1.59431i	3.09803	−	0.634191i
53.4	−1.40669	−	0.145636i	−0.834924	−	1.51753i	1.95758	+	0.409730i	−0.865605	+	2.06173i	0.953477	+	2.25630i	−0.335127			−2.69405	−	0.861458i	−1.60580	+	2.53405i	1.51790	−	2.77416i
53.5	−1.40140	+	0.189930i	−1.41275	+	1.00206i	1.92785	−	0.532336i	−1.70410	+	1.44777i	1.78951	−	1.67261i	3.47971			−2.60059	+	1.11217i	0.991748	−	2.83133i	2.11316	−	2.35257i
53.6	−1.39330	−	0.242311i	−1.15805	−	1.28799i	1.88257	+	0.675225i	0.882802	−	2.05442i	1.30142	+	2.07516i	−3.54918			−2.45937	−	1.39696i	−0.317828	+	2.98312i	−1.72782	+	2.64852i
53.7	−1.37483	−	0.331428i	0.746037	−	1.56315i	1.78031	+	0.911315i	2.23508	+	0.0665166i	−1.54374	+	1.90180i	2.63671			−2.14559	−	1.84295i	−1.88686	−	2.33233i	−3.05081	−	0.832217i
53.8	−1.37214	+	0.342392i	0.539446	−	1.64590i	1.76553	−	0.939621i	−1.78726	−	1.34376i	−0.176651	+	2.44311i	1.66623			−2.10084	+	1.89380i	−2.41800	−	1.77575i	2.91247	+	1.23188i
53.9	−1.35777	+	0.395545i	1.70665	+	0.295546i	1.68709	−	1.07412i	1.99219	−	1.01547i	−2.43414	+	0.273772i	1.72109			−1.86582	+	2.12573i	2.82530	+	1.00879i	−2.30328	+	2.16677i
53.10	−1.35181	−	0.415461i	−1.72984	+	0.0875579i	1.65478	+	1.12325i	2.16038	+	0.576859i	2.37479	+	0.600318i	3.05341			−1.77029	−	2.20592i	2.98467	−	0.302922i	−2.68076	−	1.67736i
53.11	−1.34421	+	0.439444i	−1.42675	+	0.982038i	1.61378	−	1.18141i	−1.70512	−	1.44657i	1.48629	−	1.94704i	−3.62711			−1.65009	+	2.29722i	1.07120	−	2.80224i	2.92772	+	1.19519i
53.12	−1.25726	+	0.647535i	−1.70804	−	0.287373i	1.16140	−	1.62824i	1.38621	+	1.75455i	2.33354	−	0.744716i	−3.31410			−0.405835	+	2.79916i	2.83483	+	0.981693i	−2.87895	−	1.30830i
53.13	−1.24095	+	0.678262i	−1.51810	−	0.833885i	1.07992	−	1.68338i	0.385186	−	2.20264i	2.44948	+	0.00513995i	3.88471			−0.198358	+	2.82146i	1.60927	+	2.53185i	1.01597	+	2.99463i
53.14	−1.23707	−	0.685315i	−1.73144	+	0.0458627i	1.06069	+	1.69557i	−1.82081	−	1.29794i	2.17335	+	1.12985i	−0.679704			−0.150148	−	2.82444i	2.99579	−	0.158817i	1.36297	+	2.85348i
53.15	−1.22313	−	0.709891i	1.56127	+	0.749954i	0.992110	+	1.73658i	0.587316	+	2.15756i	−1.37726	−	2.02563i	0.657556			0.0193000	−	2.82836i	1.87514	+	2.34176i	0.813264	−	3.05591i
53.16	−1.20930	+	0.733212i	1.71035	−	0.273297i	0.924802	−	1.77334i	0.643833	+	2.14137i	−1.86794	+	1.58455i	2.93776			0.181875	+	2.82257i	2.85062	−	0.934870i	−2.34867	−	2.11749i
53.17	−1.19998	−	0.748360i	0.0155491	+	1.73198i	0.879914	+	1.79604i	−2.18599	+	0.470596i	1.27749	−	2.08998i	−1.28528			0.288203	−	2.81371i	−2.99952	+	0.0538617i	2.97532	+	1.07120i
53.18	−1.18567	−	0.770833i	1.46312	−	0.926973i	0.811633	+	1.82791i	0.256821	−	2.22127i	−2.44932	−	0.0287361i	0.502977			0.446683	−	2.79293i	1.28144	−	2.71255i	−2.01673	+	2.43573i
53.19	−1.10714	+	0.879913i	0.564518	−	1.63747i	0.451505	−	1.94837i	−0.436335	+	2.19308i	0.815836	+	2.30963i	0.251991			1.21452	+	2.55440i	−2.36264	−	1.84877i	−1.44664	−	2.81198i
53.20	−1.08915	+	0.902080i	0.414542	+	1.68171i	0.372503	−	1.96500i	−1.33220	−	1.79590i	−1.96854	−	1.45769i	0.873040			1.36688	+	2.47622i	−2.65631	+	1.39428i	3.07101	+	0.754258i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
160.bb	odd	8	1	inner
480.cb	even	8	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	480.2.cb.a	yes	368
3.b	odd	2	1	inner	480.2.cb.a	yes	368
5.c	odd	4	1		480.2.br.a	✓	368
15.e	even	4	1		480.2.br.a	✓	368
32.g	even	8	1		480.2.br.a	✓	368
96.p	odd	8	1		480.2.br.a	✓	368
160.bb	odd	8	1	inner	480.2.cb.a	yes	368
480.cb	even	8	1	inner	480.2.cb.a	yes	368

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
480.2.br.a	✓	368	5.c	odd	4	1
480.2.br.a	✓	368	15.e	even	4	1
480.2.br.a	✓	368	32.g	even	8	1
480.2.br.a	✓	368	96.p	odd	8	1
480.2.cb.a	yes	368	1.a	even	1	1	trivial
480.2.cb.a	yes	368	3.b	odd	2	1	inner
480.2.cb.a	yes	368	160.bb	odd	8	1	inner
480.2.cb.a	yes	368	480.cb	even	8	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(480, [\chi])\).