Newform orbit 855.2.s.a

• Label: 855.2.s.a
• Level: $855$
• Weight: $2$
• Character orbit: 855.s
• 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.s (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.

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
49.1		−	2.78051i	1.22673	−	1.22275i	−5.73125			−1.14437	+	1.92105i	−3.39988	−	3.41095i	−2.44832	+	1.41354i			10.3748i	0.00975665	−	2.99998i	5.34150	+	3.18193i
49.2		−	2.74345i	−1.72780	+	0.121242i	−5.52654			0.486344	−	2.18254i	0.332623	+	4.74015i	−1.46938	+	0.848348i			9.67490i	2.97060	−	0.418965i	−5.98769	−	1.33426i
49.3		−	2.73282i	−1.09318	+	1.34349i	−5.46830			1.36165	+	1.77367i	3.67151	+	2.98746i	−1.62972	+	0.940918i			9.47823i	−0.609926	−	2.93734i	4.84712	−	3.72115i
49.4		−	2.64851i	0.459959	+	1.66986i	−5.01463			1.75010	−	1.39182i	4.42265	−	1.21821i	3.10566	−	1.79305i			7.98429i	−2.57688	+	1.53613i	−3.68624	−	4.63517i
49.5		−	2.60890i	−1.43994	−	0.962586i	−4.80637			0.408716	+	2.19840i	−2.51129	+	3.75666i	3.04365	−	1.75725i			7.32154i	1.14686	+	2.77213i	5.73540	−	1.06630i
49.6		−	2.59878i	1.51885	+	0.832516i	−4.75366			−2.21275	−	0.322086i	2.16353	−	3.94717i	0.834324	−	0.481697i			7.15615i	1.61383	+	2.52894i	−0.837030	+	5.75045i
49.7		−	2.55504i	−1.17264	−	1.27472i	−4.52822			−2.23396	−	0.0971468i	−3.25696	+	2.99615i	−1.86729	+	1.07808i			6.45971i	−0.249820	+	2.98958i	−0.248214	+	5.70785i
49.8		−	2.52403i	1.60815	+	0.643303i	−4.37072			−0.0888930	−	2.23430i	1.62371	−	4.05903i	−2.62968	+	1.51825i			5.98375i	2.17232	+	2.06906i	−5.63944	+	0.224368i
49.9		−	2.50954i	−0.111533	−	1.72846i	−4.29779			2.22977	+	0.167718i	−4.33763	+	0.279896i	0.287799	−	0.166161i			5.76640i	−2.97512	+	0.385560i	0.420896	−	5.59569i
49.10		−	2.50840i	−1.08359	+	1.35124i	−4.29205			−2.20665	+	0.361515i	3.38943	+	2.71807i	3.62710	−	2.09411i			5.74937i	−0.651676	−	2.92836i	0.906823	+	5.53515i
49.11		−	2.37929i	1.54586	−	0.781230i	−3.66104			2.11850	−	0.715514i	−1.85878	−	3.67805i	1.36859	−	0.790155i			3.95210i	1.77936	−	2.41534i	−1.70242	−	5.04053i
49.12		−	2.35496i	1.06629	+	1.36492i	−3.54586			1.85212	+	1.25286i	3.21435	−	2.51108i	−3.59061	+	2.07304i			3.64045i	−0.726037	+	2.91082i	2.95043	−	4.36168i
49.13		−	2.27458i	1.72833	−	0.113401i	−3.17370			1.33004	+	1.79750i	−0.257938	−	3.93123i	−0.431864	+	0.249337i			2.66968i	2.97428	−	0.391988i	4.08855	−	3.02528i
49.14		−	2.25124i	0.492454	+	1.66057i	−3.06809			−0.559537	+	2.16493i	3.73834	−	1.10863i	0.656911	−	0.379268i			2.40453i	−2.51498	+	1.63551i	4.87378	+	1.25965i
49.15		−	2.22295i	−0.439101	+	1.67547i	−2.94150			−1.35161	−	1.78134i	3.72448	+	0.976098i	−1.30755	+	0.754912i			2.09291i	−2.61438	−	1.47140i	−3.95982	+	3.00455i
49.16		−	2.18479i	0.144682	−	1.72600i	−2.77332			−1.96893	−	1.05987i	−3.77095	−	0.316100i	−0.138311	+	0.0798541i			1.68955i	−2.95813	−	0.499442i	−2.31560	+	4.30170i
49.17		−	2.16794i	0.703658	−	1.58268i	−2.69996			−1.08069	+	1.95758i	−3.43115	−	1.52549i	3.98272	−	2.29943i			1.51747i	−2.00973	−	2.22733i	4.24391	+	2.34286i
49.18		−	2.15863i	−1.36040	−	1.07206i	−2.65969			2.23478	−	0.0758165i	−2.31419	+	2.93659i	−4.12771	+	2.38314i			1.42402i	0.701359	+	2.91686i	−0.163660	−	4.82407i
49.19		−	2.09234i	−1.67476	+	0.441773i	−2.37788			−0.794129	−	2.09030i	0.924338	+	3.50417i	1.42646	−	0.823569i			0.790648i	2.60967	−	1.47973i	−4.37362	+	1.66159i
49.20		−	2.08770i	1.14638	−	1.29839i	−2.35850			−0.251212	−	2.22191i	−2.71066	−	2.39329i	−4.28952	+	2.47655i			0.748438i	−0.371645	−	2.97689i	−4.63869	+	0.524456i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
171.h	even	3	1	inner
855.s	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.s.a	✓	232
5.b	even	2	1	inner	855.2.s.a	✓	232
9.c	even	3	1		855.2.bk.a	yes	232
19.c	even	3	1		855.2.bk.a	yes	232
45.j	even	6	1		855.2.bk.a	yes	232
95.i	even	6	1		855.2.bk.a	yes	232
171.h	even	3	1	inner	855.2.s.a	✓	232
855.s	even	6	1	inner	855.2.s.a	✓	232

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
855.2.s.a	✓	232	1.a	even	1	1	trivial
855.2.s.a	✓	232	5.b	even	2	1	inner
855.2.s.a	✓	232	171.h	even	3	1	inner
855.2.s.a	✓	232	855.s	even	6	1	inner
855.2.bk.a	yes	232	9.c	even	3	1
855.2.bk.a	yes	232	19.c	even	3	1
855.2.bk.a	yes	232	45.j	even	6	1
855.2.bk.a	yes	232	95.i	even	6	1

Hecke kernels

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