Newform orbit 855.2.cz.a

• Label: 855.2.cz.a
• Level: $855$
• Weight: $2$
• Character orbit: 855.cz
• Analytic conductor: $6.827$
• Analytic rank: $0$
• Dimension: $696$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.cz (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.82720937282\)
Analytic rank:	\(0\)
Dimension:	\(696\)
Relative dimension:	\(116\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 696 q - 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
14.1	−1.77614	+	2.11672i	1.51097	−	0.846736i	−0.978542	−	5.54959i	−1.54846	−	1.61316i	−0.891397	+	4.70223i	−2.46545	−	1.42343i	8.69899	+	5.02236i	1.56608	−	2.55879i	6.16489	−	0.412452i
14.2	−1.76414	+	2.10241i	−1.58681	+	0.694292i	−0.960677	−	5.44827i	1.87700	−	1.21527i	1.33966	−	4.56095i	1.39961	+	0.808064i	8.39566	+	4.84724i	2.03592	−	2.20341i	−0.756278	+	6.09013i
14.3	−1.71799	+	2.04742i	−1.17262	−	1.27474i	−0.893139	−	5.06524i	−1.95207	+	1.09061i	4.62447	−	0.210851i	3.46780	+	2.00214i	7.27579	+	4.20068i	−0.249930	+	2.98957i	1.12069	−	5.87035i
14.4	−1.70294	+	2.02948i	−0.0545835	−	1.73119i	−0.871504	−	4.94255i	0.873283	−	2.05849i	3.60637	+	2.83733i	1.45981	+	0.842821i	6.92620	+	3.99884i	−2.99404	+	0.188989i	2.69052	+	5.27779i
14.5	−1.68283	+	2.00552i	0.951558	+	1.44725i	−0.842888	−	4.78025i	−2.21135	−	0.331573i	−4.50379	−	0.527109i	1.83271	+	1.05812i	6.47077	+	3.73590i	−1.18907	+	2.75429i	4.38629	−	3.87691i
14.6	−1.68210	+	2.00465i	−1.60863	−	0.642108i	−0.841859	−	4.77442i	1.22127	+	1.87310i	3.99308	−	2.14465i	−3.40312	−	1.96480i	6.45455	+	3.72654i	2.17540	+	2.06583i	−5.80920	−	0.702537i
14.7	−1.64122	+	1.95593i	0.705083	+	1.58204i	−0.784757	−	4.45058i	1.44263	−	1.70846i	−4.25155	−	1.21738i	−0.160015	−	0.0923848i	5.57054	+	3.21616i	−2.00572	+	2.23094i	0.973959	+	5.62562i
14.8	−1.62873	+	1.94105i	−0.797598	+	1.53748i	−0.767598	−	4.35326i	−1.43402	+	1.71569i	−1.68524	−	4.05231i	−1.31230	−	0.757658i	5.31133	+	3.06650i	−1.72768	−	2.45258i	−0.994612	−	5.57789i
14.9	−1.60758	+	1.91584i	0.760442	−	1.55619i	−0.738831	−	4.19012i	−0.235270	+	2.22366i	1.75894	+	3.95859i	−1.31478	−	0.759090i	4.88355	+	2.81952i	−1.84345	−	2.36679i	−3.88195	−	4.02545i
14.10	−1.54282	+	1.83866i	1.65654	+	0.505843i	−0.653086	−	3.70384i	2.20079	−	0.395653i	−3.48582	+	2.26539i	−4.16840	−	2.40663i	3.66043	+	2.11335i	2.48824	+	1.67590i	−2.66795	+	4.65692i
14.11	−1.53614	+	1.83070i	−0.699278	+	1.58462i	−0.644441	−	3.65480i	−0.626608	−	2.14648i	−1.82677	−	3.71436i	−3.41261	−	1.97027i	3.54153	+	2.04470i	−2.02202	−	2.21617i	4.89211	+	2.15016i
14.12	−1.51114	+	1.80091i	−1.18229	+	1.26578i	−0.612427	−	3.47325i	1.04367	+	1.97756i	−0.492948	−	4.04197i	2.60897	+	1.50629i	3.10856	+	1.79473i	−0.204391	−	2.99303i	−5.13855	−	1.10881i
14.13	−1.50851	+	1.79777i	−1.56326	−	0.745802i	−0.609084	−	3.45429i	−0.715069	−	2.11865i	3.69897	−	1.68533i	−1.42633	−	0.823492i	3.06401	+	1.76900i	1.88756	+	2.33176i	4.88753	+	1.91047i
14.14	−1.46406	+	1.74480i	0.525134	+	1.65053i	−0.553555	−	3.13937i	2.04894	+	0.895466i	−3.64866	−	1.50022i	2.70425	+	1.56130i	2.34296	+	1.35271i	−2.44847	+	1.73349i	−4.56218	+	2.26397i
14.15	−1.42588	+	1.69930i	1.73161	−	0.0389454i	−0.507183	−	2.87638i	−0.193815	−	2.22765i	−2.40289	+	2.99806i	3.61440	+	2.08678i	1.76884	+	1.02124i	2.99697	−	0.134877i	4.06180	+	2.84702i
14.16	−1.40874	+	1.67887i	1.39325	−	1.02901i	−0.486763	−	2.76057i	2.23338	+	0.109709i	−0.235154	+	3.78869i	−0.222994	−	0.128745i	1.52439	+	0.880105i	0.882286	−	2.86733i	−3.33043	+	3.59500i
14.17	−1.36140	+	1.62245i	1.58033	+	0.708916i	−0.431650	−	2.44801i	−0.0758389	+	2.23478i	−3.30165	+	1.59889i	0.240473	+	0.138837i	0.891010	+	0.514425i	1.99487	+	2.24064i	−3.52258	−	3.16548i
14.18	−1.34790	+	1.60636i	−0.762023	−	1.55542i	−0.416276	−	2.36082i	−1.93409	−	1.12219i	3.52570	+	0.872458i	−1.41860	−	0.819030i	0.721389	+	0.416494i	−1.83864	+	2.37053i	4.40960	−	1.59424i
14.19	−1.33489	+	1.59086i	1.37265	−	1.05633i	−0.401612	−	2.27765i	−1.89785	+	1.18244i	−0.151868	+	3.59379i	3.74330	+	2.16120i	0.562552	+	0.324790i	0.768341	−	2.89994i	0.652334	−	4.59765i
14.20	−1.28192	+	1.52773i	−1.61982	+	0.613343i	−0.343348	−	1.94722i	−1.51571	−	1.64396i	1.13945	−	3.26089i	3.34053	+	1.92865i	−0.0392757	−	0.0226758i	2.24762	−	1.98701i	4.45454	−	0.208176i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
171.x	even	18	1	inner
855.cz	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	855.2.cz.a	yes	696
5.b	even	2	1	inner	855.2.cz.a	yes	696
9.d	odd	6	1		855.2.co.a	✓	696
19.f	odd	18	1		855.2.co.a	✓	696
45.h	odd	6	1		855.2.co.a	✓	696
95.o	odd	18	1		855.2.co.a	✓	696
171.x	even	18	1	inner	855.2.cz.a	yes	696
855.cz	even	18	1	inner	855.2.cz.a	yes	696

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
855.2.co.a	✓	696	9.d	odd	6	1
855.2.co.a	✓	696	19.f	odd	18	1
855.2.co.a	✓	696	45.h	odd	6	1
855.2.co.a	✓	696	95.o	odd	18	1
855.2.cz.a	yes	696	1.a	even	1	1	trivial
855.2.cz.a	yes	696	5.b	even	2	1	inner
855.2.cz.a	yes	696	171.x	even	18	1	inner
855.2.cz.a	yes	696	855.cz	even	18	1	inner

Hecke kernels

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