Newform orbit 864.2.bi.a

• Label: 864.2.bi.a
• Level: $864$
• Weight: $2$
• Character orbit: 864.bi
• Analytic conductor: $6.899$
• Analytic rank: $0$
• Dimension: $216$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bi (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.89907473464\)
Analytic rank:	\(0\)
Dimension:	\(216\)
Relative dimension:	\(36\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
95.1		0		−1.72799	+	0.118502i		0		1.85973	−	2.21633i		0		−0.235484	+	0.646986i		0		2.97191	−	0.409541i		0
95.2		0		−1.70911	−	0.280941i		0		−1.54632	+	1.84283i		0		0.573007	−	1.57432i		0		2.84214	+	0.960320i		0
95.3		0		−1.69887	+	0.337423i		0		−0.948003	+	1.12979i		0		−0.391368	+	1.07528i		0		2.77229	−	1.14647i		0
95.4		0		−1.68666	−	0.393943i		0		2.16279	−	2.57751i		0		0.669796	−	1.84025i		0		2.68962	+	1.32889i		0
95.5		0		−1.59297	−	0.680026i		0		−0.802661	+	0.956575i		0		−1.53564	+	4.21915i		0		2.07513	+	2.16653i		0
95.6		0		−1.54765	+	0.777684i		0		−1.51205	+	1.80199i		0		0.535936	−	1.47247i		0		1.79042	−	2.40716i		0
95.7		0		−1.46065	+	0.930864i		0		0.902634	−	1.07572i		0		1.52652	−	4.19407i		0		1.26699	−	2.71933i		0
95.8		0		−1.37511	+	1.05313i		0		−2.70735	+	3.22649i		0		−1.09514	+	3.00888i		0		0.781832	−	2.89633i		0
95.9		0		−1.29799	−	1.14683i		0		−0.251563	+	0.299801i		0		0.212073	−	0.582665i		0		0.369555	+	2.97715i		0
95.10		0		−1.23859	+	1.21074i		0		1.02326	−	1.21948i		0		−0.575400	+	1.58090i		0		0.0682160	−	2.99922i		0
95.11		0		−1.18010	−	1.26782i		0		1.50278	−	1.79094i		0		−1.53224	+	4.20980i		0		−0.214731	+	2.99231i		0
95.12		0		−0.948095	−	1.44952i		0		0.639391	−	0.761997i		0		1.09080	−	2.99694i		0		−1.20223	+	2.74857i		0
95.13		0		−0.639313	+	1.60974i		0		1.25880	−	1.50018i		0		−0.917368	+	2.52045i		0		−2.18256	−	2.05826i		0
95.14		0		−0.633406	−	1.61208i		0		−2.10172	+	2.50473i		0		1.57289	−	4.32148i		0		−2.19759	+	2.04220i		0
95.15		0		−0.413006	+	1.68209i		0		−2.09970	+	2.50233i		0		0.771995	−	2.12104i		0		−2.65885	−	1.38943i		0
95.16		0		−0.246052	+	1.71448i		0		0.0151145	−	0.0180127i		0		1.23843	−	3.40255i		0		−2.87892	−	0.843705i		0
95.17		0		−0.152734	+	1.72530i		0		−0.204383	+	0.243574i		0		0.388373	−	1.06705i		0		−2.95334	−	0.527025i		0
95.18		0		−0.0609182	−	1.73098i		0		2.80925	−	3.34793i		0		−0.417699	+	1.14762i		0		−2.99258	+	0.210896i		0
95.19		0		0.0609182	+	1.73098i		0		2.80925	−	3.34793i		0		0.417699	−	1.14762i		0		−2.99258	+	0.210896i		0
95.20		0		0.152734	−	1.72530i		0		−0.204383	+	0.243574i		0		−0.388373	+	1.06705i		0		−2.95334	−	0.527025i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
27.f	odd	18	1	inner
108.l	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	864.2.bi.a	✓	216
4.b	odd	2	1	inner	864.2.bi.a	✓	216
27.f	odd	18	1	inner	864.2.bi.a	✓	216
108.l	even	18	1	inner	864.2.bi.a	✓	216

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
864.2.bi.a	✓	216	1.a	even	1	1	trivial
864.2.bi.a	✓	216	4.b	odd	2	1	inner
864.2.bi.a	✓	216	27.f	odd	18	1	inner
864.2.bi.a	✓	216	108.l	even	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(864, [\chi])\).