Newform orbit 532.2.ce.a

• Label: 532.2.ce.a
• Level: $532$
• Weight: $2$
• Character orbit: 532.ce
• Analytic conductor: $4.248$
• Analytic rank: $0$
• Dimension: $456$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	532.ce (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.24804138753\)
Analytic rank:	\(0\)
Dimension:	\(456\)
Relative dimension:	\(76\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 456 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
51.1	−1.41406	+	0.0206620i	−0.0462478	−	0.262284i	1.99915	−	0.0584346i	1.91670	+	0.697622i	0.0708166	+	0.369931i	2.59488	+	0.516348i	−2.82571	+	0.123937i	2.75242	−	1.00180i	−2.72475	−	0.946879i
51.2	−1.41261	−	0.0674264i	0.537414	+	3.04783i	1.99091	+	0.190494i	2.22589	+	0.810159i	−0.553650	−	4.34161i	1.65836	+	2.06151i	−2.79952	−	0.403332i	−6.18135	+	2.24983i	−3.08968	−	1.29452i
51.3	−1.41227	+	0.0740403i	0.389563	+	2.20932i	1.98904	−	0.209130i	−3.65043	−	1.32865i	−0.713748	−	3.09132i	0.687727	−	2.55481i	−2.79358	+	0.442618i	−1.91026	+	0.695276i	5.25378	+	1.60614i
51.4	−1.40171	+	0.187620i	−0.334679	−	1.89806i	1.92960	−	0.525978i	−0.819532	−	0.298285i	0.825238	+	2.59774i	2.26182	−	1.37265i	−2.60606	+	1.09930i	−0.671548	+	0.244424i	1.20471	+	0.264350i
51.5	−1.38135	+	0.303109i	0.334679	+	1.89806i	1.81625	−	0.837399i	−0.819532	−	0.298285i	−1.03763	−	2.52044i	−2.26182	+	1.37265i	−2.25505	+	1.70726i	−0.671548	+	0.244424i	1.22247	+	0.163628i
51.6	−1.35243	+	0.413451i	−0.389563	−	2.20932i	1.65812	−	1.11832i	−3.65043	−	1.32865i	1.44030	+	2.82688i	−0.687727	+	2.55481i	−1.78011	+	2.19800i	−1.91026	+	0.695276i	5.48627	+	0.287625i
51.7	−1.34706	−	0.430601i	0.171686	+	0.973682i	1.62917	+	1.16009i	−2.00664	−	0.730358i	0.187996	−	1.38554i	0.419715	+	2.61225i	−1.69505	−	2.26424i	1.90050	−	0.691725i	2.38858	+	1.84790i
51.8	−1.33585	+	0.464222i	0.0462478	+	0.262284i	1.56900	−	1.24026i	1.91670	+	0.697622i	−0.183538	−	0.328904i	−2.59488	−	0.516348i	−1.52019	+	2.38517i	2.75242	−	1.00180i	−2.88428	−	0.0421445i
51.9	−1.33397	−	0.469604i	−0.0258790	−	0.146767i	1.55894	+	1.25287i	−1.37097	−	0.498991i	−0.0344006	+	0.207936i	−2.54971	−	0.706391i	−1.49123	−	2.40338i	2.79821	−	1.01846i	1.59450	+	1.30945i
51.10	−1.30825	−	0.537094i	0.00503233	+	0.0285398i	1.42306	+	1.40531i	3.59575	+	1.30874i	0.00874496	−	0.0400401i	−0.0904702	−	2.64420i	−1.10694	−	2.60282i	2.81829	−	1.02577i	−4.00123	−	3.64342i
51.11	−1.30435	+	0.546500i	−0.537414	−	3.04783i	1.40268	−	1.42566i	2.22589	+	0.810159i	2.36661	+	3.68175i	−1.65836	−	2.06151i	−1.05046	+	2.62612i	−6.18135	+	2.24983i	−3.34610	+	0.159716i
51.12	−1.28457	−	0.591500i	−0.410632	−	2.32881i	1.30026	+	1.51965i	3.08669	+	1.12346i	−0.850004	+	3.23442i	−1.86349	+	1.87814i	−0.771403	−	2.72120i	−2.43566	+	0.886509i	−3.30055	−	3.26895i
51.13	−1.28337	−	0.594107i	−0.552147	−	3.13138i	1.29407	+	1.52492i	−0.689223	−	0.250857i	−1.15177	+	4.34675i	2.46852	−	0.952064i	−0.754809	−	2.72585i	−6.68160	+	2.43190i	0.735491	+	0.731414i
51.14	−1.15798	−	0.811833i	0.522170	+	2.96138i	0.681854	+	1.88018i	0.477303	+	0.173724i	1.79948	−	3.85314i	−1.84449	−	1.89681i	0.736817	−	2.73077i	−5.67801	+	2.06662i	−0.411674	−	0.588660i
51.15	−1.14556	−	0.829277i	0.287679	+	1.63151i	0.624598	+	1.89997i	−0.180326	−	0.0656335i	1.02342	−	2.10755i	2.21179	−	1.45189i	0.860088	−	2.69448i	0.240009	−	0.0873560i	0.152146	+	0.224727i
51.16	−1.11855	+	0.865356i	−0.171686	−	0.973682i	0.502319	−	1.93589i	−2.00664	−	0.730358i	1.03462	+	0.940545i	−0.419715	−	2.61225i	1.11336	+	2.60008i	1.90050	−	0.691725i	2.87655	−	0.919515i
51.17	−1.09291	+	0.897527i	0.0258790	+	0.146767i	0.388890	−	1.96183i	−1.37097	−	0.498991i	−0.160011	−	0.137176i	2.54971	+	0.706391i	1.33577	+	2.49313i	2.79821	−	1.01846i	1.94620	−	0.685130i
51.18	−1.05343	−	0.943551i	−0.229855	−	1.30357i	0.219423	+	1.98793i	−0.850688	−	0.309625i	−0.987851	+	1.59010i	1.15821	+	2.37877i	1.64456	−	2.30118i	1.17261	−	0.426795i	0.603992	+	1.12884i
51.19	−1.04566	+	0.952152i	−0.00503233	−	0.0285398i	0.186812	−	1.99126i	3.59575	+	1.30874i	0.0324363	+	0.0250514i	0.0904702	+	2.64420i	1.70064	+	2.26005i	2.81829	−	1.02577i	−5.00605	+	2.05520i
51.20	−1.00480	+	0.995178i	0.410632	+	2.32881i	0.0192426	−	1.99991i	3.08669	+	1.12346i	−2.73018	−	1.93134i	1.86349	−	1.87814i	1.97093	+	2.02866i	−2.43566	+	0.886509i	−4.21955	+	1.94295i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
133.bd	odd	18	1	inner
532.ce	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	532.2.ce.a	yes	456
4.b	odd	2	1	inner	532.2.ce.a	yes	456
7.c	even	3	1		532.2.bs.a	✓	456
19.f	odd	18	1		532.2.bs.a	✓	456
28.g	odd	6	1		532.2.bs.a	✓	456
76.k	even	18	1		532.2.bs.a	✓	456
133.bd	odd	18	1	inner	532.2.ce.a	yes	456
532.ce	even	18	1	inner	532.2.ce.a	yes	456

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
532.2.bs.a	✓	456	7.c	even	3	1
532.2.bs.a	✓	456	19.f	odd	18	1
532.2.bs.a	✓	456	28.g	odd	6	1
532.2.bs.a	✓	456	76.k	even	18	1
532.2.ce.a	yes	456	1.a	even	1	1	trivial
532.2.ce.a	yes	456	4.b	odd	2	1	inner
532.2.ce.a	yes	456	133.bd	odd	18	1	inner
532.2.ce.a	yes	456	532.ce	even	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(532, [\chi])\).