Newform orbit 819.2.cm.a

• Label: 819.2.cm.a
• Level: $819$
• Weight: $2$
• Character orbit: 819.cm
• Analytic conductor: $6.540$
• Analytic rank: $0$
• Dimension: $216$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.cm (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.53974792554\)
Analytic rank:	\(0\)
Dimension:	\(216\)
Relative dimension:	\(108\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 216 q + 3 q^{2} - 3 q^{3} - 105 q^{4} - 12 q^{8} + 3 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
257.1	−1.40864	−	2.43983i	−0.946532	−	1.45054i	−2.96852	+	5.14163i	−2.98800	+	1.72512i	−2.20576	+	4.35267i	2.24028	−	1.40753i	11.0917			−1.20815	+	2.74597i	8.41801	+	4.86014i
257.2	−1.35275	−	2.34304i	−1.72450	−	0.161576i	−2.65988	+	4.60704i	2.33791	−	1.34979i	1.95424	+	4.25913i	−2.46238	+	0.967819i	8.98161			2.94779	+	0.557273i	−6.32523	−	3.65187i
257.3	−1.32420	−	2.29359i	1.30542	+	1.13836i	−2.50703	+	4.34230i	−3.09602	+	1.78749i	0.882294	−	4.50152i	−2.63127	−	0.276445i	7.98244			0.408253	+	2.97209i	8.19952	+	4.73399i
257.4	−1.31788	−	2.28263i	−0.860823	+	1.50299i	−2.47359	+	4.28439i	−1.05855	+	0.611154i	4.56523	−	0.0158186i	1.66807	+	2.05366i	7.76804			−1.51797	−	2.58762i	2.79007	+	1.61085i
257.5	−1.30925	−	2.26769i	1.28131	+	1.16543i	−2.42829	+	4.20592i	0.0958954	−	0.0553653i	0.965279	−	4.43147i	1.23084	+	2.34202i	7.47996			0.283532	+	2.98657i	−0.251103	−	0.144974i
257.6	−1.30745	−	2.26457i	1.67960	−	0.423036i	−2.41886	+	4.18959i	1.11626	−	0.644475i	−3.15399	−	3.25047i	1.61487	−	2.09576i	7.42036			2.64208	−	1.42106i	−2.91892	−	1.68524i
257.7	−1.27985	−	2.21676i	0.311881	+	1.70374i	−2.27601	+	3.94217i	2.78742	−	1.60932i	3.37762	−	2.87189i	0.221231	−	2.63649i	6.53239			−2.80546	+	1.06273i	−7.13494	−	4.11936i
257.8	−1.26499	−	2.19102i	−1.31738	+	1.12450i	−2.20038	+	3.81116i	−0.705450	+	0.407292i	4.13027	+	1.46393i	−0.688656	−	2.55456i	6.07383			0.470989	−	2.96280i	1.78477	+	1.03044i
257.9	−1.19014	−	2.06138i	−0.981948	−	1.42681i	−1.83286	+	3.17461i	2.15363	−	1.24340i	−1.77254	+	3.72227i	1.62056	+	2.09136i	3.96490			−1.07156	+	2.80210i	−5.12623	−	2.95963i
257.10	−1.18481	−	2.05215i	1.73180	+	0.0294234i	−1.80753	+	3.13074i	3.37811	−	1.95035i	−1.99147	−	3.58877i	−1.11830	+	2.39779i	3.82708			2.99827	+	0.101911i	−8.00480	−	4.62158i
257.11	−1.18435	−	2.05135i	0.594852	−	1.62670i	−1.80535	+	3.12697i	−0.518676	+	0.299458i	−4.04144	+	0.706327i	−0.921772	+	2.47999i	3.81527			−2.29230	−	1.93529i	1.22858	+	0.709324i
257.12	−1.16015	−	2.00943i	1.18404	−	1.26414i	−1.69188	+	2.93043i	−1.25810	+	0.726364i	−3.91387	−	0.912670i	2.42392	+	1.06047i	3.21075			−0.196087	−	2.99358i	2.91916	+	1.68538i
257.13	−1.11244	−	1.92681i	−1.64662	−	0.537252i	−1.47506	+	2.55488i	−2.78532	+	1.60810i	0.796590	+	3.77039i	−1.79484	+	1.94385i	2.11391			2.42272	+	1.76930i	6.19701	+	3.57785i
257.14	−1.09243	−	1.89215i	−0.638300	−	1.61015i	−1.38682	+	2.40203i	−0.285391	+	0.164771i	−2.34934	+	2.96673i	−2.22112	−	1.43757i	1.69028			−2.18515	+	2.05551i	0.623540	+	0.360001i
257.15	−1.07455	−	1.86117i	0.145698	−	1.72591i	−1.30931	+	2.26779i	2.12173	−	1.22498i	−3.36878	+	1.58341i	1.90054	−	1.84064i	1.32946			−2.95754	−	0.502924i	−4.55981	−	2.63261i
257.16	−1.01646	−	1.76055i	1.10907	+	1.33040i	−1.06636	+	1.84700i	0.934501	−	0.539535i	1.21493	−	3.30487i	−2.19210	−	1.48145i	0.269825			−0.539941	+	2.95101i	−1.89976	−	1.09683i
257.17	−1.01431	−	1.75683i	−1.51695	−	0.835980i	−1.05764	+	1.83189i	−0.183357	+	0.105861i	0.0699780	+	3.51297i	−1.52275	−	2.16361i	0.233878			1.60228	+	2.53628i	0.371962	+	0.214752i
257.18	−1.01032	−	1.74993i	−1.50108	+	0.864160i	−1.04151	+	1.80395i	2.70058	−	1.55918i	3.02880	+	1.75370i	2.62040	+	0.365369i	0.167762			1.50645	−	2.59434i	−5.45693	−	3.15056i
257.19	−0.998585	−	1.72960i	−0.199965	+	1.72047i	−0.994344	+	1.72226i	−1.82979	+	1.05643i	3.17541	−	1.37218i	−2.36166	+	1.19271i	−0.0225900			−2.92003	−	0.688066i	3.65440	+	2.10987i
257.20	−0.995132	−	1.72362i	1.62529	+	0.598694i	−0.980575	+	1.69841i	−2.47431	+	1.42854i	−0.585457	−	3.39716i	2.18693	−	1.48907i	−0.0773215			2.28313	+	1.94610i	4.92452	+	2.84317i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
819.cm	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	819.2.cm.a	yes	216
7.d	odd	6	1		819.2.ea.a	yes	216
9.d	odd	6	1		819.2.bs.a	✓	216
13.e	even	6	1		819.2.cc.a	yes	216
63.i	even	6	1		819.2.cc.a	yes	216
91.l	odd	6	1		819.2.bs.a	✓	216
117.m	odd	6	1		819.2.ea.a	yes	216
819.cm	even	6	1	inner	819.2.cm.a	yes	216

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
819.2.bs.a	✓	216	9.d	odd	6	1
819.2.bs.a	✓	216	91.l	odd	6	1
819.2.cc.a	yes	216	13.e	even	6	1
819.2.cc.a	yes	216	63.i	even	6	1
819.2.cm.a	yes	216	1.a	even	1	1	trivial
819.2.cm.a	yes	216	819.cm	even	6	1	inner
819.2.ea.a	yes	216	7.d	odd	6	1
819.2.ea.a	yes	216	117.m	odd	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(819, [\chi])\).