Newform orbit 855.2.t.a

• Label: 855.2.t.a
• Level: $855$
• Weight: $2$
• Character orbit: 855.t
• Analytic conductor: $6.827$
• Analytic rank: $0$
• Dimension: $232$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.82720937282\)
Analytic rank:	\(0\)
Dimension:	\(232\)
Relative dimension:	\(116\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 232 q - 228 q^{4} - 3 q^{5} + 14 q^{6} - 2 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
164.1		−	2.73759i	1.63815	−	0.562551i	−5.49438			1.89416	−	1.18833i	−1.54003	−	4.48458i	3.67033	+	2.11907i			9.56616i	2.36707	−	1.84309i	−3.25317	−	5.18544i
164.2		−	2.73250i	−1.68619	+	0.395930i	−5.46658			2.20888	−	0.347636i	1.08188	+	4.60752i	−1.95703	−	1.12989i			9.47243i	2.68648	−	1.33523i	−0.949916	−	6.03577i
164.3		−	2.71274i	−1.72743	−	0.126384i	−5.35893			−1.32427	+	1.80175i	−0.342846	+	4.68607i	3.32996	+	1.92255i			9.11190i	2.96805	+	0.436639i	4.88768	+	3.59239i
164.4		−	2.71121i	0.545129	+	1.64403i	−5.35067			1.53820	+	1.62294i	4.45731	−	1.47796i	−1.24030	−	0.716087i			9.08437i	−2.40567	+	1.79242i	4.40014	−	4.17038i
164.5		−	2.66178i	−0.0931240	−	1.72955i	−5.08505			−1.61878	−	1.54258i	−4.60366	+	0.247875i	0.704988	+	0.407025i			8.21172i	−2.98266	+	0.322125i	−4.10600	+	4.30883i
164.6		−	2.61675i	1.55650	+	0.759808i	−4.84741			−2.01356	+	0.972406i	1.98823	−	4.07298i	−0.225642	−	0.130274i			7.45096i	1.84538	+	2.36528i	2.54455	+	5.26900i
164.7		−	2.61268i	−0.993059	+	1.41910i	−4.82608			−2.15070	−	0.611940i	3.70764	+	2.59454i	−3.85492	−	2.22564i			7.38362i	−1.02767	−	2.81849i	−1.59880	+	5.61909i
164.8		−	2.56936i	0.442159	+	1.67466i	−4.60161			0.152761	−	2.23084i	4.30281	−	1.13607i	1.25137	+	0.722479i			6.68448i	−2.60899	+	1.48093i	−5.73184	−	0.392498i
164.9		−	2.45888i	1.24864	−	1.20038i	−4.04607			0.608861	+	2.15158i	−2.95158	−	3.07024i	−2.97922	−	1.72005i			5.03103i	0.118187	−	2.99767i	5.29046	−	1.49711i
164.10		−	2.39463i	0.723747	−	1.57359i	−3.73426			1.59534	−	1.56681i	−3.76817	−	1.73311i	−3.53648	−	2.04179i			4.15292i	−1.95238	−	2.27776i	−3.75194	−	3.82024i
164.11		−	2.34965i	−0.992727	−	1.41933i	−3.52084			−1.71035	+	1.44038i	−3.33492	+	2.33256i	−3.13722	−	1.81128i			3.57344i	−1.02899	+	2.81801i	3.38440	+	4.01871i
164.12		−	2.34340i	−1.18395	−	1.26422i	−3.49154			1.67249	−	1.48417i	−2.96259	+	2.77447i	0.512676	+	0.295994i			3.49527i	−0.196526	+	2.99356i	−3.47802	−	3.91932i
164.13		−	2.29693i	−1.20131	+	1.24774i	−3.27587			−1.28035	−	1.83322i	2.86596	+	2.75933i	1.78790	+	1.03224i			2.93058i	−0.113686	−	2.99785i	−4.21077	+	2.94088i
164.14		−	2.27993i	−1.12034	−	1.32093i	−3.19807			1.89538	+	1.18639i	−3.01162	+	2.55429i	1.54089	+	0.889632i			2.73151i	−0.489692	+	2.95976i	2.70489	−	4.32133i
164.15		−	2.24494i	1.43266	−	0.973387i	−3.03976			−2.15314	−	0.603299i	−2.18519	−	3.21624i	−0.0552195	−	0.0318810i			2.33420i	1.10504	−	2.78907i	−1.35437	+	4.83368i
164.16		−	2.22799i	1.73021	−	0.0797670i	−2.96394			0.970786	+	2.01434i	−0.177720	−	3.85490i	0.671550	+	0.387720i			2.14764i	2.98727	−	0.276028i	4.48793	−	2.16290i
164.17		−	2.16894i	−0.754156	+	1.55925i	−2.70431			2.20205	+	0.388541i	3.38191	+	1.63572i	3.93283	+	2.27062i			1.52760i	−1.86250	−	2.35183i	0.842723	−	4.77612i
164.18		−	2.16404i	1.13465	+	1.30865i	−2.68308			0.385543	−	2.20258i	2.83198	−	2.45542i	−1.71387	−	0.989501i			1.47821i	−0.425153	+	2.96972i	−4.76647	−	0.834331i
164.19		−	2.11284i	0.207190	+	1.71961i	−2.46408			−1.45456	+	1.69831i	3.63327	−	0.437760i	1.48259	+	0.855974i			0.980535i	−2.91414	+	0.712575i	3.58826	+	3.07324i
164.20		−	2.03785i	−1.72884	+	0.105455i	−2.15283			1.08542	+	1.95496i	0.214902	+	3.52311i	−2.17641	−	1.25655i			0.311446i	2.97776	−	0.364630i	3.98391	−	2.21193i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
171.t	even	6	1	inner
855.t	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	855.2.t.a	✓	232
5.b	even	2	1	inner	855.2.t.a	✓	232
9.d	odd	6	1		855.2.bm.a	yes	232
19.d	odd	6	1		855.2.bm.a	yes	232
45.h	odd	6	1		855.2.bm.a	yes	232
95.h	odd	6	1		855.2.bm.a	yes	232
171.t	even	6	1	inner	855.2.t.a	✓	232
855.t	even	6	1	inner	855.2.t.a	✓	232

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
855.2.t.a	✓	232	1.a	even	1	1	trivial
855.2.t.a	✓	232	5.b	even	2	1	inner
855.2.t.a	✓	232	171.t	even	6	1	inner
855.2.t.a	✓	232	855.t	even	6	1	inner
855.2.bm.a	yes	232	9.d	odd	6	1
855.2.bm.a	yes	232	19.d	odd	6	1
855.2.bm.a	yes	232	45.h	odd	6	1
855.2.bm.a	yes	232	95.h	odd	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(855, [\chi])\).