Newform orbit 960.2.cn.a

• Label: 960.2.cn.a
• Level: $960$
• Weight: $2$
• Character orbit: 960.cn
• Analytic conductor: $7.666$
• Analytic rank: $0$
• Dimension: $1024$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.cn (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.66563859404\)
Analytic rank:	\(0\)
Dimension:	\(1024\)
Relative dimension:	\(128\) over \(\Q(\zeta_{16})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1024 q+O(q^{10}) \)

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	−1.41007	+	0.108158i	−1.47205	−	0.912721i	1.97660	−	0.305021i	−0.831470	+	0.555570i	2.17442	+	1.12779i	−0.940518	+	2.27061i	−2.75416	+	0.643887i	1.33388	+	2.68715i	1.11234	−	0.873324i
11.2	−1.40951	−	0.115188i	−1.54582	+	0.781298i	1.97346	+	0.324719i	0.831470	−	0.555570i	2.26886	−	0.923189i	0.523119	−	1.26292i	−2.74422	−	0.685017i	1.77915	−	2.41550i	−1.23596	+	0.687309i
11.3	−1.40773	−	0.135291i	−1.72878	−	0.106455i	1.96339	+	0.380905i	0.831470	−	0.555570i	2.41924	+	0.383747i	−1.61857	+	3.90758i	−2.71239	−	0.801839i	2.97733	+	0.368073i	−1.24565	+	0.669601i
11.4	−1.40630	+	0.149381i	−1.62091	−	0.610439i	1.95537	−	0.420150i	−0.831470	+	0.555570i	2.37068	+	0.616328i	0.941598	−	2.27322i	−2.68708	+	0.882954i	2.25473	+	1.97894i	1.08631	−	0.905505i
11.5	−1.40439	+	0.166429i	1.12802	−	1.31437i	1.94460	−	0.467462i	−0.831470	+	0.555570i	−1.36543	+	2.03362i	−1.59037	+	3.83950i	−2.65317	+	0.980137i	−0.455120	−	2.96528i	1.07524	−	0.918616i
11.6	−1.39615	−	0.225336i	1.73045	−	0.0744627i	1.89845	+	0.629205i	−0.831470	+	0.555570i	−2.43274	−	0.285972i	0.198700	−	0.479704i	−2.50873	−	1.30625i	2.98891	−	0.257708i	1.28604	−	0.588297i
11.7	−1.39425	+	0.236792i	1.62205	−	0.607410i	1.88786	−	0.660293i	0.831470	−	0.555570i	−2.11771	+	1.23097i	1.55710	−	3.75918i	−2.47579	+	1.36764i	2.26211	−	1.97050i	−1.02772	+	0.971488i
11.8	−1.39236	−	0.247642i	0.171669	−	1.72352i	1.87735	+	0.689615i	−0.831470	+	0.555570i	−0.665842	+	2.35726i	1.85931	−	4.48877i	−2.44317	−	1.42510i	−2.94106	−	0.591749i	1.29529	−	0.567648i
11.9	−1.39036	−	0.258642i	0.964034	+	1.43897i	1.86621	+	0.719212i	−0.831470	+	0.555570i	−0.968177	−	2.25003i	1.69186	−	4.08451i	−2.40869	−	1.48264i	−1.14128	+	2.77444i	1.29974	−	0.557390i
11.10	−1.38297	−	0.295641i	−0.109184	+	1.72861i	1.82519	+	0.817723i	−0.831470	+	0.555570i	0.662044	−	2.35833i	−1.07535	+	2.59612i	−2.28243	−	1.67048i	−2.97616	−	0.377472i	1.31414	−	0.522519i
11.11	−1.37738	+	0.320672i	0.686468	−	1.59021i	1.79434	−	0.883374i	0.831470	−	0.555570i	−0.435591	+	2.41045i	−1.11347	+	2.68816i	−2.18821	+	1.79213i	−2.05752	−	2.18325i	−0.967092	+	1.03186i
11.12	−1.35801	−	0.394728i	0.491468	−	1.66086i	1.68838	+	1.07209i	0.831470	−	0.555570i	−1.32301	+	2.06147i	−0.0610195	+	0.147314i	−1.86965	−	2.12236i	−2.51692	−	1.63252i	−1.34844	+	0.426266i
11.13	−1.34932	+	0.423483i	−0.184888	+	1.72215i	1.64132	−	1.14283i	0.831470	−	0.555570i	−0.479831	−	2.40203i	−1.27921	+	3.08829i	−1.73070	+	2.23711i	−2.93163	−	0.636812i	−0.886643	+	1.10176i
11.14	−1.33543	−	0.465441i	1.35701	+	1.07635i	1.56673	+	1.24312i	0.831470	−	0.555570i	−1.31121	−	2.06899i	0.233451	−	0.563601i	−1.51365	−	2.38932i	0.682956	+	2.92123i	−1.36895	+	0.354923i
11.15	−1.31971	+	0.508299i	1.68975	+	0.380451i	1.48327	−	1.34161i	0.831470	−	0.555570i	−2.42336	+	0.356813i	−0.283377	+	0.684133i	−1.27554	+	2.52448i	2.71051	+	1.28573i	−0.814903	+	1.15583i
11.16	−1.31762	−	0.513694i	−1.22944	+	1.22003i	1.47224	+	1.35371i	−0.831470	+	0.555570i	2.24665	−	0.975986i	−0.119152	+	0.287657i	−1.24446	−	2.53995i	0.0230310	−	2.99991i	1.38095	−	0.304909i
11.17	−1.31358	+	0.523935i	−1.24256	−	1.20667i	1.45098	−	1.37646i	0.831470	−	0.555570i	2.26441	+	0.934041i	0.421755	−	1.01821i	−1.18481	+	2.56831i	0.0878878	+	2.99871i	−0.801119	+	1.16542i
11.18	−1.29199	−	0.575126i	−1.21242	−	1.23695i	1.33846	+	1.48611i	0.831470	−	0.555570i	0.855032	+	2.29541i	1.27656	−	3.08189i	−0.874572	−	2.68982i	−0.0600719	+	2.99940i	−1.39377	+	0.239590i
11.19	−1.29008	+	0.579386i	−1.30752	+	1.13596i	1.32862	−	1.49491i	−0.831470	+	0.555570i	1.02864	−	2.22304i	−1.57931	+	3.81278i	−0.847903	+	2.69834i	0.419195	−	2.97057i	0.750774	−	1.19847i
11.20	−1.28704	+	0.586117i	−0.793124	+	1.53979i	1.31293	−	1.50871i	−0.831470	+	0.555570i	0.118283	−	2.44663i	1.18065	−	2.85033i	−0.805513	+	2.71130i	−1.74191	−	2.44249i	0.744504	−	1.20238i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
64.j	odd	16	1	inner
192.s	even	16	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	960.2.cn.a	✓	1024
3.b	odd	2	1	inner	960.2.cn.a	✓	1024
64.j	odd	16	1	inner	960.2.cn.a	✓	1024
192.s	even	16	1	inner	960.2.cn.a	✓	1024

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
960.2.cn.a	✓	1024	1.a	even	1	1	trivial
960.2.cn.a	✓	1024	3.b	odd	2	1	inner
960.2.cn.a	✓	1024	64.j	odd	16	1	inner
960.2.cn.a	✓	1024	192.s	even	16	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(960, [\chi])\).