Newform orbit 855.2.w.a

• Label: 855.2.w.a
• Level: $855$
• Weight: $2$
• Character orbit: 855.w
• Analytic conductor: $6.827$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(6.82720937282\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(80\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 160 q - 80 q^{4} + 4 q^{6} + 4 q^{7} - 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
56.1	−1.38690	+	2.40218i	1.57257	−	0.725969i	−2.84698	−	4.93111i	0.866025	−	0.500000i	−0.437085	+	4.78444i	2.26462	−	3.92245i	10.2463			1.94594	−	2.28327i			2.77380i
56.2	−1.37029	+	2.37341i	−1.25718	+	1.19143i	−2.75539	−	4.77247i	−0.866025	+	0.500000i	−1.10506	−	4.61640i	−1.84976	+	3.20388i	9.62156			0.160981	−	2.99568i		−	2.74058i
56.3	−1.34161	+	2.32374i	−0.432730	+	1.67712i	−2.59983	−	4.50304i	0.866025	−	0.500000i	−3.31664	−	3.25560i	0.271573	−	0.470377i	8.58541			−2.62549	−	1.45148i			2.68322i
56.4	−1.31129	+	2.27122i	0.456273	−	1.67087i	−2.43896	−	4.22441i	0.866025	−	0.500000i	3.19661	+	3.22730i	−1.58687	+	2.74854i	7.54760			−2.58363	−	1.52475i			2.62258i
56.5	−1.27301	+	2.20491i	1.63470	−	0.572499i	−2.24109	−	3.88169i	−0.866025	+	0.500000i	−0.818676	+	4.33317i	−0.693265	+	1.20077i	6.31968			2.34449	−	1.87173i		−	2.54601i
56.6	−1.22636	+	2.12411i	−1.50827	−	0.851547i	−2.00790	−	3.47778i	0.866025	−	0.500000i	3.65845	−	2.15943i	−0.232832	+	0.403277i	4.94416			1.54974	+	2.56872i			2.45271i
56.7	−1.20480	+	2.08677i	−1.69503	+	0.356185i	−1.90309	−	3.29624i	−0.866025	+	0.500000i	1.29890	−	3.96628i	1.39715	−	2.41993i	4.35215			2.74626	−	1.20749i		−	2.40960i
56.8	−1.19990	+	2.07828i	0.750776	−	1.56088i	−1.87950	−	3.25539i	−0.866025	+	0.500000i	2.34309	+	3.43321i	−0.294714	+	0.510459i	4.22123			−1.87267	−	2.34374i		−	2.39979i
56.9	−1.19827	+	2.07546i	0.557079	+	1.64002i	−1.87170	−	3.24187i	−0.866025	+	0.500000i	−4.07133	−	0.808989i	1.17919	−	2.04242i	4.17811			−2.37933	+	1.82724i		−	2.39654i
56.10	−1.16327	+	2.01484i	1.13713	+	1.30650i	−1.70638	−	2.95555i	0.866025	−	0.500000i	−3.95517	+	0.771334i	1.39031	−	2.40809i	3.28686			−0.413861	+	2.97132i			2.32654i
56.11	−1.15860	+	2.00676i	−0.245106	−	1.71462i	−1.68472	−	2.91802i	−0.866025	+	0.500000i	3.72481	+	1.49470i	2.29492	−	3.97492i	3.17328			−2.87985	+	0.840527i		−	2.31721i
56.12	−1.07513	+	1.86219i	−1.46131	−	0.929817i	−1.31183	−	2.27215i	−0.866025	+	0.500000i	3.30260	−	1.72156i	−2.38146	+	4.12480i	1.34102			1.27088	+	2.71751i		−	2.15027i
56.13	−1.03881	+	1.79927i	−1.16362	+	1.28296i	−1.15825	−	2.00615i	0.866025	−	0.500000i	−1.09962	−	3.42642i	−0.691007	+	1.19686i	0.657563			−0.291982	−	2.98576i			2.07762i
56.14	−1.03554	+	1.79360i	−0.444537	−	1.67403i	−1.14467	−	1.98263i	0.866025	−	0.500000i	3.46288	+	0.936200i	−0.538667	+	0.932998i	0.599242			−2.60477	+	1.48834i			2.07107i
56.15	−0.965535	+	1.67236i	1.70969	−	0.277442i	−0.864515	−	1.49738i	−0.866025	+	0.500000i	−1.18678	+	3.12708i	−0.855216	+	1.48128i	−0.523262			2.84605	−	0.948678i		−	1.93107i
56.16	−0.950900	+	1.64701i	1.71879	+	0.213880i	−0.808421	−	1.40023i	0.866025	−	0.500000i	−1.98666	+	2.62749i	0.0418973	−	0.0725683i	−0.728692			2.90851	+	0.735233i			1.90180i
56.17	−0.896853	+	1.55339i	1.64845	+	0.531621i	−0.608690	−	1.05428i	−0.866025	+	0.500000i	−2.30423	+	2.08390i	2.06105	−	3.56984i	−1.40379			2.43476	+	1.75270i		−	1.79371i
56.18	−0.893999	+	1.54845i	−1.72282	+	0.178569i	−0.598470	−	1.03658i	0.866025	−	0.500000i	1.26370	−	2.82735i	−1.57618	+	2.73003i	−1.43587			2.93623	−	0.615284i			1.78800i
56.19	−0.825924	+	1.43054i	−0.943610	+	1.45245i	−0.364302	−	0.630990i	−0.866025	+	0.500000i	−1.29844	−	2.54949i	1.01351	−	1.75546i	−2.10015			−1.21920	−	2.74109i		−	1.65185i
56.20	−0.795188	+	1.37731i	−1.35625	−	1.07731i	−0.264647	−	0.458381i	0.866025	−	0.500000i	2.56225	−	1.01131i	1.88645	−	3.26742i	−2.33898			0.678817	+	2.92219i			1.59038i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.d	odd	6	1	inner
19.b	odd	2	1	inner
171.l	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.w.a	✓	160
9.d	odd	6	1	inner	855.2.w.a	✓	160
19.b	odd	2	1	inner	855.2.w.a	✓	160
171.l	even	6	1	inner	855.2.w.a	✓	160

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
855.2.w.a	✓	160	1.a	even	1	1	trivial
855.2.w.a	✓	160	9.d	odd	6	1	inner
855.2.w.a	✓	160	19.b	odd	2	1	inner
855.2.w.a	✓	160	171.l	even	6	1	inner

Hecke kernels

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