Newform orbit 663.2.ck.a

• Label: 663.2.ck.a
• Level: $663$
• Weight: $2$
• Character orbit: 663.ck
• Analytic conductor: $5.294$
• Analytic rank: $0$
• Dimension: $640$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 663 = 3 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	663.ck (of order \(24\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.29408165401\)
Analytic rank:	\(0\)
Dimension:	\(640\)
Relative dimension:	\(80\) over \(\Q(\zeta_{24})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 640 q - 4 q^{3} + 304 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−2.42969	+	1.40278i	−1.72931	+	0.0973549i	2.93560	−	5.08460i	−0.316141	+	0.763232i	4.06513	−	2.66239i	−0.516497	+	3.92318i			10.8609i	2.98104	−	0.336714i	−0.302524	−	2.29790i
2.2	−2.31486	+	1.33649i	1.18978	−	1.25874i	2.57240	−	4.45553i	−0.871501	+	2.10399i	−1.07189	+	4.50394i	−0.143628	+	1.09096i			8.40597i	−0.168851	−	2.99524i	−0.794549	−	6.03520i
2.3	−2.30724	+	1.33209i	1.38556	+	1.03934i	2.54890	−	4.41483i	0.105152	−	0.253859i	−4.58131	−	0.552308i	0.182161	−	1.38365i			8.25309i	0.839565	+	2.88013i	0.0955513	+	0.725785i
2.4	−2.24562	+	1.29651i	−0.780982	+	1.54598i	2.36186	−	4.09086i	1.69578	−	4.09397i	−0.250593	−	4.48423i	0.361749	−	2.74775i			7.06264i	−1.78013	−	2.41477i	1.49980	+	11.3921i
2.5	−2.22554	+	1.28491i	−0.487934	−	1.66190i	2.30201	−	3.98719i	1.37690	−	3.32413i	3.22132	+	3.07167i	−0.332154	+	2.52296i			6.69187i	−2.52384	+	1.62180i	1.20688	+	9.16718i
2.6	−2.14452	+	1.23814i	0.749392	−	1.56154i	2.06598	−	3.57839i	0.371739	−	0.897457i	0.326319	+	4.27661i	0.594835	−	4.51822i			5.27935i	−1.87682	−	2.34041i	0.313976	+	2.38488i
2.7	−2.09897	+	1.21184i	−1.16738	−	1.27954i	1.93710	−	3.35516i	0.216771	−	0.523331i	4.00088	+	1.27105i	0.229692	−	1.74468i			4.54247i	−0.274469	+	2.98742i	0.179198	+	1.36114i
2.8	−2.05538	+	1.18667i	−1.32878	−	1.11101i	1.81639	−	3.14609i	−1.45538	+	3.51361i	4.04956	+	0.706719i	0.386156	−	2.93314i			3.87518i	0.531314	+	2.95258i	−1.17814	−	8.94887i
2.9	−1.99854	+	1.15386i	1.66652	−	0.471926i	1.66277	−	2.88001i	0.813791	−	1.96467i	−2.78607	+	2.86609i	−0.217444	+	1.65165i			3.05898i	2.55457	−	1.57295i	0.640550	+	4.86546i
2.10	−1.97239	+	1.13876i	1.66553	+	0.475412i	1.59355	−	2.76011i	−1.48433	+	3.58350i	−3.82645	+	0.958939i	−0.0918090	+	0.697359i			2.70364i	2.54797	+	1.58362i	−1.15306	−	8.75836i
2.11	−1.96896	+	1.13678i	0.981689	+	1.42699i	1.58454	−	2.74450i	0.917185	−	2.21428i	−3.55508	−	1.69371i	−0.653577	+	4.96441i			2.65797i	−1.07257	+	2.80171i	0.711248	+	5.40247i
2.12	−1.94974	+	1.12568i	−1.59411	+	0.677347i	1.53432	−	2.65752i	−0.00373534	+	0.00901790i	2.34563	−	3.11512i	0.280554	−	2.13102i			2.40590i	2.08240	−	2.15954i	−0.00286836	−	0.0217873i
2.13	−1.84101	+	1.06291i	−1.37916	+	1.04782i	1.25954	−	2.18159i	−0.451509	+	1.09004i	1.42531	−	3.39496i	0.0208920	−	0.158690i			1.10347i	0.804158	−	2.89021i	−0.327378	−	2.48668i
2.14	−1.72418	+	0.995454i	−0.502017	+	1.65770i	0.981856	−	1.70062i	−1.45907	+	3.52251i	−0.784600	−	3.35791i	−0.540709	+	4.10709i		−	0.0722477i	−2.49596	−	1.66439i	−0.990798	−	7.52586i
2.15	−1.64857	+	0.951804i	1.73145	+	0.0455020i	0.811863	−	1.40619i	1.25166	−	3.02176i	−2.89774	+	1.57299i	0.300819	−	2.28494i		−	0.716278i	2.99586	+	0.157569i	0.812681	+	6.17293i
2.16	−1.62719	+	0.939458i	0.569445	−	1.63577i	0.765164	−	1.32530i	−0.178440	+	0.430793i	0.610140	+	3.19667i	−0.304797	+	2.31517i		−	0.882473i	−2.35147	−	1.86296i	−0.114356	−	0.868618i
2.17	−1.52996	+	0.883321i	−1.73095	−	0.0616978i	0.560513	−	0.970837i	1.20214	−	2.90223i	2.70278	−	1.43459i	−0.325510	+	2.47249i		−	1.55283i	2.99239	+	0.213592i	0.724373	+	5.50216i
2.18	−1.46427	+	0.845396i	0.145236	+	1.72595i	0.429387	−	0.743721i	−0.342636	+	0.827196i	−1.67178	−	2.40447i	0.425222	−	3.22988i		−	1.92957i	−2.95781	+	0.501340i	−0.197597	−	1.50090i
2.19	−1.40521	+	0.811300i	−0.0343814	−	1.73171i	0.316416	−	0.548049i	−1.19143	+	2.87636i	1.45325	+	2.40553i	−0.0339696	+	0.258024i		−	2.21837i	−2.99764	+	0.119077i	−0.659382	−	5.00851i
2.20	−1.39639	+	0.806208i	0.875937	+	1.49423i	0.299943	−	0.519516i	0.103697	−	0.250347i	−2.42782	−	1.38035i	0.462208	−	3.51081i		−	2.25757i	−1.46547	+	2.61771i	0.0570298	+	0.433185i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
221.bc	odd	24	1	inner
663.ck	even	24	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	663.2.ck.a	yes	640
3.b	odd	2	1	inner	663.2.ck.a	yes	640
13.f	odd	12	1		663.2.cf.a	✓	640
17.d	even	8	1		663.2.cf.a	✓	640
39.k	even	12	1		663.2.cf.a	✓	640
51.g	odd	8	1		663.2.cf.a	✓	640
221.bc	odd	24	1	inner	663.2.ck.a	yes	640
663.ck	even	24	1	inner	663.2.ck.a	yes	640

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
663.2.cf.a	✓	640	13.f	odd	12	1
663.2.cf.a	✓	640	17.d	even	8	1
663.2.cf.a	✓	640	39.k	even	12	1
663.2.cf.a	✓	640	51.g	odd	8	1
663.2.ck.a	yes	640	1.a	even	1	1	trivial
663.2.ck.a	yes	640	3.b	odd	2	1	inner
663.2.ck.a	yes	640	221.bc	odd	24	1	inner
663.2.ck.a	yes	640	663.ck	even	24	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(663, [\chi])\).