Newform orbit 335.2.w.a

• Label: 335.2.w.a
• Level: $335$
• Weight: $2$
• Character orbit: 335.w
• Analytic conductor: $2.675$
• Analytic rank: $0$
• Dimension: $1280$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 335 = 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	335.w (of order \(132\), degree \(40\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.67498846771\)
Analytic rank:	\(0\)
Dimension:	\(1280\)
Relative dimension:	\(32\) over \(\Q(\zeta_{132})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{132}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1280 q - 38 q^{2} - 44 q^{3} - 44 q^{5} - 80 q^{6} - 38 q^{7} - 110 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−1.87425	−	2.06175i	−0.728004	−	1.33324i	−0.547868	+	5.73753i	1.29736	−	1.82122i	−1.38434	+	3.99979i	0.706985	−	2.21164i	8.39504	−	6.28445i	0.374384	−	0.582553i	−6.18649	+	0.738608i
2.2	−1.71233	−	1.88362i	0.923973	+	1.69213i	−0.425859	+	4.45980i	1.82956	+	1.28558i	1.60519	−	4.63789i	−0.501820	+	1.56983i	5.05407	−	3.78343i	−0.387654	+	0.603201i	−0.711243	−	5.64753i
2.3	−1.68278	−	1.85112i	1.22437	+	2.24227i	−0.404787	+	4.23912i	−2.19152	−	0.444101i	2.09037	−	6.03972i	1.35933	−	4.25235i	4.52291	−	3.38581i	−1.90678	+	2.96700i	2.86577	+	4.80410i
2.4	−1.58453	−	1.74304i	−1.25172	−	2.29235i	−0.337346	+	3.53285i	−1.49883	+	1.65937i	−2.01227	+	5.81408i	−0.00628661	+	0.0196662i	2.92090	−	2.18656i	−2.06614	+	3.21497i	5.26729	−	0.0168081i
2.5	−1.50050	−	1.65060i	−0.0676603	−	0.123911i	−0.282886	+	2.96252i	−1.01373	−	1.99308i	−0.103003	+	0.297608i	−0.545203	+	1.70554i	1.74289	−	1.30471i	1.61115	−	2.50699i	−1.76869	+	4.66387i
2.6	−1.35588	−	1.49151i	−0.450295	−	0.824655i	−0.196101	+	2.05367i	1.81517	+	1.30582i	−0.619439	+	1.78975i	−0.426030	+	1.33274i	0.101672	−	0.0761104i	1.14463	−	1.78108i	−0.513486	−	4.47788i
2.7	−1.11051	−	1.22160i	0.752678	+	1.37843i	−0.0689651	+	0.722235i	1.55695	−	1.60496i	0.848029	−	2.45022i	0.531865	−	1.66382i	−1.68438	+	1.26091i	0.288386	−	0.448737i	−3.68962	−	0.119649i
2.8	−1.08643	−	1.19511i	0.477842	+	0.875103i	−0.0578534	+	0.605868i	−2.23143	−	0.143905i	0.526705	−	1.52181i	−1.01846	+	3.18601i	−1.79901	+	1.34672i	1.08445	−	1.68744i	2.25231	+	2.82316i
2.9	−1.08050	−	1.18859i	1.50186	+	2.75045i	−0.0551539	+	0.577598i	−0.203774	+	2.22676i	1.64640	−	4.75695i	−0.253409	+	0.792734i	−1.82571	+	1.36671i	−3.68747	+	5.73781i	2.86689	−	2.16381i
2.10	−1.02849	−	1.13137i	−1.52168	−	2.78674i	−0.0321095	+	0.336266i	0.451888	−	2.18993i	−1.58782	+	4.58771i	−1.31940	+	4.12745i	−2.03456	+	1.52306i	−3.82850	+	5.95726i	−2.94239	+	1.74106i
2.11	−0.926393	−	1.01907i	−0.00752523	−	0.0137814i	0.00981925	−	0.102832i	−0.980825	+	2.00947i	−0.00707287	+	0.0204357i	1.12515	−	3.51976i	−2.31891	+	1.73592i	1.62179	−	2.52355i	2.95642	−	0.862036i
2.12	−0.775382	−	0.852949i	−0.958841	−	1.75599i	0.0638075	−	0.668222i	−2.11931	−	0.713096i	−0.754298	+	2.17940i	1.22621	−	3.83592i	−2.46502	+	1.84529i	−0.542187	+	0.843660i	1.03504	+	2.36059i
2.13	−0.471157	−	0.518290i	−0.637076	−	1.16672i	0.143476	−	1.50255i	−0.111677	+	2.23328i	−0.304535	+	0.879897i	−1.41662	+	4.43156i	−1.96782	+	1.47309i	0.666559	−	1.03719i	1.21010	−	0.994343i
2.14	−0.438879	−	0.482783i	−0.748732	−	1.37120i	0.149647	−	1.56718i	0.395439	−	2.20082i	−0.333390	+	0.963266i	0.701460	−	2.19436i	−1.86691	+	1.39755i	0.302332	−	0.470438i	−1.23607	+	0.774984i
2.15	−0.197596	−	0.217363i	1.10696	+	2.02725i	0.181910	−	1.90504i	2.22634	−	0.208367i	0.221918	−	0.641190i	−1.52429	+	4.76840i	−0.920353	+	0.688968i	−1.26246	+	1.96443i	−0.485207	−	0.442751i
2.16	−0.173696	−	0.191073i	−0.850181	−	1.55699i	0.183774	−	1.92457i	2.08783	+	0.800609i	−0.149825	+	0.432890i	0.268681	−	0.840506i	−0.813089	+	0.608671i	−0.0794885	+	0.123687i	−0.209674	−	0.537990i
2.17	−0.00997829	−	0.0109765i	0.109887	+	0.201243i	0.190091	−	1.99072i	−1.22223	−	1.87247i	0.00111246	−	0.00321424i	−0.560754	+	1.75419i	−0.0474985	+	0.0355570i	1.59350	−	2.47953i	−0.00835736	+	0.0320999i
2.18	0.0653356	+	0.0718716i	1.37436	+	2.51695i	0.189215	−	1.98155i	−0.534949	−	2.17114i	−0.0911025	+	0.263223i	0.782496	−	2.44786i	0.310293	−	0.232283i	−2.82424	+	4.39460i	0.121092	−	0.180300i
2.19	0.0676170	+	0.0743813i	0.649168	+	1.18886i	0.189152	−	1.98088i	1.97647	+	1.04575i	−0.0445343	+	0.128673i	1.09579	−	3.42793i	0.321074	−	0.240353i	0.629947	−	0.980217i	0.0558588	+	0.217722i
2.20	0.418693	+	0.460578i	−0.107784	−	0.197392i	0.153284	−	1.60526i	−1.35831	+	1.77623i	0.0457858	−	0.132289i	−0.0559963	+	0.175172i	1.80011	−	1.34755i	1.59458	−	2.48121i	−1.38681	+	0.118087i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
67.h	odd	66	1	inner
335.w	even	132	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	335.2.w.a	✓	1280
5.c	odd	4	1	inner	335.2.w.a	✓	1280
67.h	odd	66	1	inner	335.2.w.a	✓	1280
335.w	even	132	1	inner	335.2.w.a	✓	1280

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
335.2.w.a	✓	1280	1.a	even	1	1	trivial
335.2.w.a	✓	1280	5.c	odd	4	1	inner
335.2.w.a	✓	1280	67.h	odd	66	1	inner
335.2.w.a	✓	1280	335.w	even	132	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(335, [\chi])\).