Newform orbit 819.2.ce.a

• Label: 819.2.ce.a
• Level: $819$
• Weight: $2$
• Character orbit: 819.ce
• Analytic conductor: $6.540$
• Analytic rank: $0$
• Dimension: $216$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.ce (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.

\(\operatorname{Tr}(f)(q) = \) \( 216 q - 108 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
272.1	−1.37374	+	2.37939i	−1.73106	+	0.0585131i	−2.77433	−	4.80528i	1.80216	−	1.04048i	2.23881	−	4.19925i	−1.76514	−	1.97086i	9.74986			2.99315	−	0.202580i			5.71738i
272.2	−1.37374	+	2.37939i	1.73106	−	0.0585131i	−2.77433	−	4.80528i	−1.80216	+	1.04048i	−2.23881	+	4.19925i	−2.58938	−	0.543229i	9.74986			2.99315	−	0.202580i		−	5.71738i
272.3	−1.37198	+	2.37633i	−0.181315	+	1.72253i	−2.76463	−	4.78849i	1.19116	−	0.687715i	−3.84455	−	2.79414i	−0.875107	+	2.49684i	9.68414			−2.93425	−	0.624644i			3.77412i
272.4	−1.37198	+	2.37633i	0.181315	−	1.72253i	−2.76463	−	4.78849i	−1.19116	+	0.687715i	3.84455	+	2.79414i	1.72477	−	2.00628i	9.68414			−2.93425	−	0.624644i		−	3.77412i
272.5	−1.28482	+	2.22538i	−1.54885	+	0.775281i	−2.30154	−	3.98638i	−3.74738	+	2.16355i	0.264707	−	4.44288i	0.515695	+	2.59501i	6.68898			1.79788	−	2.40159i		−	11.1191i
272.6	−1.28482	+	2.22538i	1.54885	−	0.775281i	−2.30154	−	3.98638i	3.74738	−	2.16355i	−0.264707	+	4.44288i	2.50519	−	0.850898i	6.68898			1.79788	−	2.40159i			11.1191i
272.7	−1.23571	+	2.14031i	−1.29205	−	1.15352i	−2.05395	−	3.55755i	−2.25731	+	1.30326i	4.06549	−	1.33996i	−2.63571	−	0.230328i	5.20951			0.338767	+	2.98081i		−	6.44180i
272.8	−1.23571	+	2.14031i	1.29205	+	1.15352i	−2.05395	−	3.55755i	2.25731	−	1.30326i	−4.06549	+	1.33996i	−1.51732	−	2.16742i	5.20951			0.338767	+	2.98081i			6.44180i
272.9	−1.21791	+	2.10948i	−0.897268	+	1.48152i	−1.96660	−	3.40625i	0.0680484	−	0.0392877i	−2.03245	−	3.69713i	2.05250	−	1.66950i	4.70893			−1.38982	−	2.65865i			0.191395i
272.10	−1.21791	+	2.10948i	0.897268	−	1.48152i	−1.96660	−	3.40625i	−0.0680484	+	0.0392877i	2.03245	+	3.69713i	−0.419582	+	2.61227i	4.70893			−1.38982	−	2.65865i		−	0.191395i
272.11	−1.20755	+	2.09153i	−1.27562	−	1.17166i	−1.91634	−	3.31919i	2.24193	−	1.29438i	3.99094	−	1.25317i	2.05199	+	1.67014i	4.42607			0.254419	+	2.98919i			6.25209i
272.12	−1.20755	+	2.09153i	1.27562	+	1.17166i	−1.91634	−	3.31919i	−2.24193	+	1.29438i	−3.99094	+	1.25317i	2.47237	+	0.942005i	4.42607			0.254419	+	2.98919i		−	6.25209i
272.13	−1.16597	+	2.01952i	−0.784481	−	1.54421i	−1.71898	−	2.97736i	−1.23952	+	0.715638i	4.03325	+	0.216230i	0.385173	+	2.61756i	3.35323			−1.76918	+	2.42281i		−	3.33765i
272.14	−1.16597	+	2.01952i	0.784481	+	1.54421i	−1.71898	−	2.97736i	1.23952	−	0.715638i	−4.03325	−	0.216230i	2.45946	−	0.975213i	3.35323			−1.76918	+	2.42281i			3.33765i
272.15	−1.08577	+	1.88060i	−1.20413	+	1.24502i	−1.35778	−	2.35174i	−1.58572	+	0.915518i	−1.03399	−	3.61629i	−0.787653	−	2.52579i	1.55385			−0.100154	−	2.99833i		−	3.97615i
272.16	−1.08577	+	1.88060i	1.20413	−	1.24502i	−1.35778	−	2.35174i	1.58572	−	0.915518i	1.03399	+	3.61629i	−2.58122	+	0.580766i	1.55385			−0.100154	−	2.99833i			3.97615i
272.17	−1.07309	+	1.85865i	−1.72933	+	0.0970785i	−1.30306	−	2.25697i	1.30820	−	0.755292i	1.67530	−	3.31840i	−2.35901	+	1.19794i	1.30085			2.98115	−	0.335761i			3.24200i
272.18	−1.07309	+	1.85865i	1.72933	−	0.0970785i	−1.30306	−	2.25697i	−1.30820	+	0.755292i	−1.67530	+	3.31840i	−0.142062	−	2.64193i	1.30085			2.98115	−	0.335761i		−	3.24200i
272.19	−0.964761	+	1.67101i	−1.08070	+	1.35355i	−0.861526	−	1.49221i	3.53823	−	2.04280i	−1.21918	−	3.11171i	0.452851	+	2.60671i	−0.534376			−0.664186	−	2.92555i			7.88325i
272.20	−0.964761	+	1.67101i	1.08070	−	1.35355i	−0.861526	−	1.49221i	−3.53823	+	2.04280i	1.21918	+	3.11171i	2.48390	−	0.911174i	−0.534376			−0.664186	−	2.92555i		−	7.88325i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
9.d	odd	6	1	inner
13.b	even	2	1	inner
63.o	even	6	1	inner
91.b	odd	2	1	inner
117.n	odd	6	1	inner
819.ce	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.ce.a	✓	216
7.b	odd	2	1	inner	819.2.ce.a	✓	216
9.d	odd	6	1	inner	819.2.ce.a	✓	216
13.b	even	2	1	inner	819.2.ce.a	✓	216
63.o	even	6	1	inner	819.2.ce.a	✓	216
91.b	odd	2	1	inner	819.2.ce.a	✓	216
117.n	odd	6	1	inner	819.2.ce.a	✓	216
819.ce	even	6	1	inner	819.2.ce.a	✓	216

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
819.2.ce.a	✓	216	1.a	even	1	1	trivial
819.2.ce.a	✓	216	7.b	odd	2	1	inner
819.2.ce.a	✓	216	9.d	odd	6	1	inner
819.2.ce.a	✓	216	13.b	even	2	1	inner
819.2.ce.a	✓	216	63.o	even	6	1	inner
819.2.ce.a	✓	216	91.b	odd	2	1	inner
819.2.ce.a	✓	216	117.n	odd	6	1	inner
819.2.ce.a	✓	216	819.ce	even	6	1	inner

Hecke kernels

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