Newform orbit 279.2.o.a

• Label: 279.2.o.a
• Level: $279$
• Weight: $2$
• Character orbit: 279.o
• Analytic conductor: $2.228$
• Analytic rank: $0$
• Dimension: $60$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	279.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.22782621639\)
Analytic rank:	\(0\)
Dimension:	\(60\)
Relative dimension:	\(30\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) 60 * q - 6 * q^2 - 3 * q^3 + 26 * q^4 - 9 * q^6 + q^9 - 4 * q^10 - 3 * q^11 - 9 * q^12 - 3 * q^14 - 3 * q^15 - 22 * q^16 + 5 * q^18 - 4 * q^19 - 21 * q^20 + 9 * q^21 - 9 * q^23 + 18 * q^24 - 52 * q^25 + 18 * q^26 - 9 * q^27 + 4 * q^28 + 3 * q^30 - 8 * q^31 + 6 * q^32 - 27 * q^33 - 21 * q^36 - 15 * q^37 + 9 * q^39 + 16 * q^40 - 60 * q^42 + 18 * q^44 + 23 * q^45 - 9 * q^47 - 6 * q^48 + 36 * q^49 + 27 * q^50 + 27 * q^51 - 42 * q^53 - 15 * q^55 + 3 * q^57 + 9 * q^58 + 36 * q^59 + 30 * q^60 - 21 * q^61 + 45 * q^62 - 43 * q^63 - 26 * q^64 + 72 * q^65 - 24 * q^66 - 10 * q^67 - 30 * q^68 - 54 * q^69 + 13 * q^70 - 9 * q^71 + 58 * q^72 + 15 * q^73 - 66 * q^74 + 12 * q^75 + 23 * q^76 - 18 * q^78 - 33 * q^80 - 23 * q^81 - 22 * q^82 + 9 * q^83 + 12 * q^84 + 15 * q^85 + 21 * q^86 - 15 * q^87 + 51 * q^88 + 36 * q^89 + 28 * q^90 + 36 * q^92 - 60 * q^93 - 28 * q^94 + 39 * q^95 + 30 * q^96 - 6 * q^97 - 177 * q^98 + 18 * q^99

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
212.1	−2.38924	+	1.37943i	0.223694	−	1.71755i	2.80566	−	4.85955i		−	2.74061i	1.83478	+	4.41221i	3.63550					9.96314i	−2.89992	−	0.768408i	3.78048	+	6.54799i
212.2	−2.24716	+	1.29740i	−1.11395	+	1.32632i	2.36648	−	4.09887i			0.842729i	0.782453	−	4.42568i	−1.64274					7.09149i	−0.518244	−	2.95490i	−1.09335	−	1.89375i
212.3	−2.05902	+	1.18877i	1.25713	−	1.19147i	1.82637	−	3.16337i			2.45958i	−1.17207	+	3.94772i	−4.44716					3.92947i	0.160776	−	2.99569i	−2.92388	−	5.06431i
212.4	−2.02036	+	1.16646i	1.47488	+	0.908139i	1.72124	−	2.98127i			3.90711i	−4.03910	−	0.114380i	3.96483					3.36517i	1.35057	+	2.67880i	−4.55747	−	7.89377i
212.5	−1.98560	+	1.14638i	0.571667	+	1.63499i	1.62840	−	2.82047i		−	2.34954i	−3.00943	−	2.59108i	1.01394					2.88154i	−2.34639	+	1.86934i	2.69347	+	4.66523i
212.6	−1.80686	+	1.04319i	−1.57828	−	0.713466i	1.17649	−	2.03774i		−	3.18672i	3.59601	−	0.357313i	−4.53398					0.736453i	1.98193	+	2.25210i	3.32435	+	5.75794i
212.7	−1.58076	+	0.912652i	−0.943804	−	1.45232i	0.665866	−	1.15331i			0.928080i	2.81739	+	1.43440i	0.680428				−	1.21979i	−1.21847	+	2.74141i	−0.847014	−	1.46707i
212.8	−1.45499	+	0.840038i	−1.65183	+	0.521020i	0.411327	−	0.712440i			0.175209i	1.96572	−	2.14568i	4.05741				−	1.97803i	2.45708	−	1.72127i	−0.147183	−	0.254928i
212.9	−1.38533	+	0.799823i	1.73203	−	0.00916385i	0.279433	−	0.483993i		−	2.80402i	−2.39211	+	1.39801i	−0.641206				−	2.30530i	2.99983	−	0.0317441i	2.24272	+	3.88451i
212.10	−1.23314	+	0.711956i	1.13852	−	1.30529i	0.0137635	−	0.0238391i			0.0916355i	−0.474647	+	2.42018i	1.83840				−	2.80863i	−0.407559	−	2.97219i	−0.0652404	−	0.113000i
212.11	−0.717067	+	0.413999i	1.45486	+	0.939887i	−0.657210	+	1.13832i			1.60091i	−1.43234	−	0.0716528i	−2.90298				−	2.74433i	1.23322	+	2.73481i	−0.662774	−	1.14796i
212.12	−0.709222	+	0.409470i	−1.73176	−	0.0319037i	−0.664669	+	1.15124i			4.31120i	1.24126	−	0.686475i	−3.40596				−	2.72653i	2.99796	+	0.110499i	−1.76530	−	3.05760i
212.13	−0.591342	+	0.341411i	−0.973017	+	1.43291i	−0.766877	+	1.32827i		−	3.24855i	0.0861734	−	1.17954i	−1.23880				−	2.41293i	−1.10647	−	2.78850i	1.10909	+	1.92100i
212.14	−0.413058	+	0.238479i	−0.421828	−	1.67990i	−0.886255	+	1.53504i			0.840842i	0.574861	+	0.593299i	−0.423978				−	1.79933i	−2.64412	+	1.41726i	−0.200523	−	0.347317i
212.15	−0.212314	+	0.122579i	−0.212705	+	1.71894i	−0.969949	+	1.68000i			2.14593i	−0.165546	−	0.391028i	2.80577				−	0.965901i	−2.90951	−	0.731255i	−0.263047	−	0.455610i
212.16	−0.0237016	+	0.0136841i	0.348190	−	1.69669i	−0.999625	+	1.73140i		−	1.80293i	0.0149651	+	0.0449790i	−3.77544				−	0.109453i	−2.75753	−	1.18154i	0.0246715	+	0.0427323i
212.17	0.130557	−	0.0753769i	1.39507	+	1.02654i	−0.988637	+	1.71237i		−	3.46214i	0.259513	+	0.0288661i	3.02237					0.599589i	0.892422	+	2.86419i	−0.260966	−	0.452006i
212.18	0.529444	−	0.305675i	1.27637	−	1.17084i	−0.813126	+	1.40838i		−	1.55166i	0.317871	−	1.01005i	4.38153					2.21691i	0.258252	−	2.98886i	−0.474304	−	0.821519i
212.19	0.657101	−	0.379377i	−1.72690	−	0.133426i	−0.712146	+	1.23347i		−	0.946287i	−1.18537	+	0.567474i	−0.758809					2.59820i	2.96440	+	0.460828i	−0.359000	−	0.621806i
212.20	0.661325	−	0.381816i	1.65931	−	0.496676i	−0.708433	+	1.22704i			3.02290i	0.907705	−	0.962016i	−1.18471					2.60923i	2.50663	−	1.64828i	1.15419	+	1.99912i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
279.o	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	279.2.o.a	✓	60
3.b	odd	2	1		837.2.o.a		60
9.c	even	3	1		837.2.r.a		60
9.d	odd	6	1		279.2.r.a	yes	60
31.e	odd	6	1		279.2.r.a	yes	60
93.g	even	6	1		837.2.r.a		60
279.n	odd	6	1		837.2.o.a		60
279.o	even	6	1	inner	279.2.o.a	✓	60

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
279.2.o.a	✓	60	1.a	even	1	1	trivial
279.2.o.a	✓	60	279.o	even	6	1	inner
279.2.r.a	yes	60	9.d	odd	6	1
279.2.r.a	yes	60	31.e	odd	6	1
837.2.o.a		60	3.b	odd	2	1
837.2.o.a		60	279.n	odd	6	1
837.2.r.a		60	9.c	even	3	1
837.2.r.a		60	93.g	even	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(279, [\chi])\).