Newform orbit 671.2.ct.a

• Label: 671.2.ct.a
• Level: $671$
• Weight: $2$
• Character orbit: 671.ct
• Analytic conductor: $5.358$
• Analytic rank: $0$
• Dimension: $480$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.ct (of order \(30\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.35796197563\)
Analytic rank:	\(0\)
Dimension:	\(480\)
Relative dimension:	\(60\) over \(\Q(\zeta_{30})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 480 q - 9 q^{2} - 2 q^{3} + 229 q^{4} - 22 q^{6} - 13 q^{7} - 114 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
97.1	−2.37955	+	1.37383i	−2.30479	−	1.67453i	2.77482	−	4.80614i	0.401104	−	3.81625i	7.78487	+	0.818223i	−0.836999	+	1.87993i			9.75323i	1.58096	+	4.86571i	4.28844	+	9.63199i
97.2	−2.34981	+	1.35666i	1.81383	+	1.31783i	2.68108	−	4.64377i	0.0865693	−	0.823652i	−6.05002	−	0.635883i	−0.258104	+	0.579712i			9.12264i	0.626274	+	1.92747i	0.913998	+	2.05287i
97.3	−2.29025	+	1.32227i	−1.40664	−	1.02198i	2.49682	−	4.32461i	−0.154775	+	1.47259i	4.57289	+	0.480630i	1.09657	−	2.46294i			7.91680i	0.00713310	+	0.0219534i	−1.59269	−	3.57724i
97.4	−2.17231	+	1.25418i	0.388788	+	0.282471i	2.14595	−	3.71690i	−0.267537	+	2.54544i	−1.19884	−	0.126003i	−1.93081	+	4.33667i			5.74895i	−0.855685	−	2.63353i	−2.61128	−	5.86503i
97.5	−2.11958	+	1.22374i	1.18509	+	0.861019i	1.99507	−	3.45557i	−0.401580	+	3.82078i	−3.56555	−	0.374755i	1.34998	−	3.03211i			4.87084i	−0.263964	−	0.812399i	−3.82446	−	8.58987i
97.6	−2.07829	+	1.19990i	1.74589	+	1.26846i	1.87952	−	3.25543i	0.281998	−	2.68304i	−5.15050	−	0.541339i	0.799851	−	1.79650i			4.22135i	0.512085	+	1.57604i	2.63330	+	5.91449i
97.7	−2.04844	+	1.18267i	−2.41200	−	1.75242i	1.79742	−	3.11322i	−0.288154	+	2.74160i	7.01338	+	0.737136i	−1.68178	+	3.77734i			3.77232i	1.81971	+	5.60050i	−2.65214	−	5.95681i
97.8	−1.98204	+	1.14433i	−0.0992895	−	0.0721381i	1.61898	−	2.80415i	0.291810	−	2.77639i	0.279345	+	0.0293603i	−1.23216	+	2.76749i			2.83325i	−0.922396	−	2.83884i	2.59872	+	5.83682i
97.9	−1.95493	+	1.12868i	−0.319942	−	0.232451i	1.54784	−	2.68094i	0.351772	−	3.34688i	0.887829	+	0.0933145i	1.89974	−	4.26688i			2.47336i	−0.878722	−	2.70443i	3.08987	+	6.93997i
97.10	−1.83013	+	1.05662i	−1.72928	−	1.25639i	1.23291	−	2.13546i	−0.0139998	+	0.133199i	4.49234	+	0.472164i	0.816500	−	1.83389i			0.984392i	0.484826	+	1.49214i	−0.115120	−	0.258564i
97.11	−1.81901	+	1.05021i	2.61470	+	1.89969i	1.20588	−	2.08864i	−0.275000	+	2.61645i	−6.75124	−	0.709584i	−0.564132	+	1.26706i			0.864851i	2.30077	+	7.08104i	−2.24759	−	5.04817i
97.12	−1.72925	+	0.998385i	0.485161	+	0.352490i	0.993546	−	1.72087i	−0.143536	+	1.36565i	−1.19089	−	0.125167i	0.926277	−	2.08045i		−	0.0257763i	−0.815919	−	2.51114i	−1.11524	−	2.50487i
97.13	−1.61498	+	0.932412i	−0.488547	−	0.354950i	0.738784	−	1.27961i	0.0768523	−	0.731201i	1.11996	+	0.117712i	−1.02845	+	2.30994i		−	0.974244i	−0.814362	−	2.50635i	0.557665	+	1.25254i
97.14	−1.40951	+	0.813780i	1.33031	+	0.966528i	0.324476	−	0.562010i	0.108199	−	1.02944i	−2.66163	−	0.279748i	−0.575619	+	1.29286i		−	2.19891i	−0.0914990	−	0.281605i	0.685234	+	1.53906i
97.15	−1.32338	+	0.764052i	0.0905404	+	0.0657815i	0.167550	−	0.290205i	−0.286928	+	2.72994i	−0.170080	−	0.0178761i	0.165530	−	0.371786i		−	2.54414i	−0.923181	−	2.84126i	−1.70610	−	3.83197i
97.16	−1.26542	+	0.730589i	−2.59705	−	1.88687i	0.0675208	−	0.116949i	0.104018	−	0.989663i	4.66487	+	0.490298i	0.868539	−	1.95077i		−	2.72504i	2.25734	+	6.94739i	0.591411	+	1.32833i
97.17	−1.19682	+	0.690985i	−1.81553	−	1.31906i	−0.0450799	+	0.0780806i	0.188761	−	1.79594i	3.08431	+	0.324174i	−1.35145	+	3.03541i		−	2.88854i	0.629172	+	1.93639i	1.01505	+	2.27985i
97.18	−1.10334	+	0.637014i	−1.51660	−	1.10187i	−0.188426	+	0.326363i	−0.370489	+	3.52497i	2.37523	+	0.249647i	0.367215	−	0.824779i		−	3.02818i	0.158890	+	0.489015i	−1.83668	−	4.12525i
97.19	−1.08694	+	0.627543i	2.31883	+	1.68473i	−0.212380	+	0.367854i	0.405510	−	3.85817i	−3.57766	−	0.376027i	−1.83445	+	4.12023i		−	3.04328i	1.61161	+	4.96003i	1.98040	+	4.44806i
97.20	−1.08676	+	0.627443i	2.73048	+	1.98381i	−0.212631	+	0.368288i	0.0171438	−	0.163112i	−4.21212	−	0.442711i	1.97386	−	4.43336i		−	3.04343i	2.59298	+	7.98037i	0.0837123	+	0.188021i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
671.ct	even	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	671.2.ct.a	yes	480
11.c	even	5	1		671.2.ch.a	✓	480
61.k	even	30	1		671.2.ch.a	✓	480
671.ct	even	30	1	inner	671.2.ct.a	yes	480

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
671.2.ch.a	✓	480	11.c	even	5	1
671.2.ch.a	✓	480	61.k	even	30	1
671.2.ct.a	yes	480	1.a	even	1	1	trivial
671.2.ct.a	yes	480	671.ct	even	30	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(671, [\chi])\).