Newform orbit 935.2.cn.a

• Label: 935.2.cn.a
• Level: $935$
• Weight: $2$
• Character orbit: 935.cn
• Analytic conductor: $7.466$
• Analytic rank: $0$
• Dimension: $3328$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.cn (of order \(80\), degree \(32\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.46601258899\)
Analytic rank:	\(0\)
Dimension:	\(3328\)
Relative dimension:	\(104\) over \(\Q(\zeta_{80})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{80}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 3328 q - 24 q^{2} - 24 q^{3} - 24 q^{5} - 48 q^{6} - 24 q^{7} + 8 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
37.1	−1.47153	−	2.40131i	0.0978560	+	0.346971i	−2.69293	+	5.28518i	2.22145	+	0.255233i	0.689188	−	0.745560i	1.44958	+	2.58842i	11.0388	−	0.868772i	2.44711	−	1.49959i	−2.65603	−	5.70999i
37.2	−1.41316	−	2.30606i	−0.385281	−	1.36610i	−2.41293	+	4.73565i	−2.22679	+	0.203512i	−2.60586	+	2.81900i	1.56600	+	2.79629i	8.93800	−	0.703436i	0.840120	−	0.514826i	3.61611	+	4.84752i
37.3	−1.40337	−	2.29009i	0.435328	+	1.54356i	−2.36709	+	4.64567i	−1.13451	−	1.92688i	2.92396	−	3.16312i	−1.08308	−	1.93397i	8.60570	−	0.677283i	0.364868	−	0.223591i	−2.82060	+	5.30227i
37.4	−1.38532	−	2.26063i	0.520066	+	1.84402i	−2.28337	+	4.48137i	−1.88997	+	1.19500i	3.44819	−	3.73023i	−1.19667	−	2.13682i	8.00762	−	0.630213i	−0.572008	+	0.350527i	5.31966	+	2.61706i
37.5	−1.38012	−	2.25216i	−0.774187	−	2.74506i	−2.25949	+	4.43450i	−1.01831	−	1.99074i	−5.11383	+	5.53211i	−1.14431	−	2.04332i	7.83906	−	0.616947i	−4.37807	+	2.68289i	−3.07807	+	5.04086i
37.6	−1.36892	−	2.23388i	−0.421702	−	1.49524i	−2.20828	+	4.33399i	0.225522	+	2.22467i	−2.76291	+	2.98890i	−2.40620	−	4.29657i	7.48081	−	0.588753i	0.500006	−	0.306404i	4.66091	−	3.54918i
37.7	−1.31922	−	2.15278i	0.835679	+	2.96309i	−1.98611	+	3.89797i	1.28512	−	1.82988i	5.27643	−	5.70801i	0.398839	+	0.712178i	5.97748	−	0.470438i	−5.52364	+	3.38489i	−5.63469	−	0.352551i
37.8	−1.29579	−	2.11454i	−0.822549	−	2.91654i	−1.88423	+	3.69802i	2.18328	+	0.483020i	−5.10130	+	5.51855i	0.378605	+	0.676047i	5.31649	−	0.418417i	−5.27170	+	3.23050i	−1.80771	−	5.24253i
37.9	−1.29091	−	2.10658i	−0.354393	−	1.25658i	−1.86324	+	3.65681i	0.724124	−	2.11557i	−2.18960	+	2.36870i	0.504200	+	0.900313i	5.18256	−	0.407877i	1.10451	−	0.676845i	−5.39140	+	1.20559i
37.10	−1.28142	−	2.09109i	0.876135	+	3.10654i	−1.82264	+	3.57713i	1.05552	+	1.97126i	5.37336	−	5.81287i	−0.226397	−	0.404261i	4.92581	−	0.387669i	−6.32505	+	3.87600i	2.76952	−	4.73321i
37.11	−1.27300	−	2.07735i	0.0221826	+	0.0786537i	−1.78687	+	3.50692i	2.19388	−	0.432333i	0.135153	−	0.146207i	−2.16011	−	3.85715i	4.70206	−	0.370060i	2.55223	−	1.56401i	−3.69091	−	4.00708i
37.12	−1.18962	−	1.94128i	0.376368	+	1.33450i	−1.44539	+	2.83675i	0.0860128	+	2.23441i	2.14291	−	2.31818i	2.29585	+	4.09954i	2.68685	−	0.211460i	0.918681	−	0.562968i	4.23530	−	2.82507i
37.13	−1.16817	−	1.90627i	0.608262	+	2.15673i	−1.36128	+	2.67167i	−2.03169	−	0.933942i	3.40077	−	3.67894i	2.41673	+	4.31539i	2.22547	−	0.175148i	−1.72360	+	1.05622i	0.592999	+	4.96395i
37.14	−1.13174	−	1.84683i	0.348029	+	1.23402i	−1.22197	+	2.39824i	−1.35913	+	1.77561i	1.88514	−	2.03933i	0.0195716	+	0.0349476i	1.49342	−	0.117535i	1.15625	−	0.708550i	4.81742	+	0.500554i
37.15	−1.11773	−	1.82397i	0.0190287	+	0.0674708i	−1.16957	+	2.29540i	−1.09626	−	1.94890i	0.101796	−	0.110122i	0.728385	+	1.30063i	1.22879	−	0.0967076i	2.55373	−	1.56493i	−2.32942	+	4.17789i
37.16	−1.11711	−	1.82295i	−0.534256	−	1.89433i	−1.16724	+	2.29084i	1.42478	+	1.72337i	−2.85645	+	3.09009i	1.50867	+	2.69392i	1.21720	−	0.0957954i	−0.745133	+	0.456618i	1.54998	−	4.52249i
37.17	−1.10558	−	1.80415i	0.217238	+	0.770269i	−1.12466	+	2.20727i	1.99158	−	1.01667i	1.14951	−	1.24353i	0.597937	+	1.06769i	1.00678	−	0.0792357i	2.01180	−	1.23283i	−4.03609	−	2.46908i
37.18	−1.08917	−	1.77737i	−0.440031	−	1.56023i	−1.06477	+	2.08972i	−2.23602	+	0.0145372i	−2.29384	+	2.48146i	−0.0487902	−	0.0871211i	0.717686	−	0.0564831i	0.317224	−	0.194395i	2.46126	+	3.95841i
37.19	−1.08412	−	1.76913i	−0.320213	−	1.13539i	−1.04651	+	2.05389i	0.844449	+	2.07048i	−1.66150	+	1.79740i	−0.556593	−	0.993869i	0.631158	−	0.0496732i	1.37135	−	0.840364i	2.74746	−	3.73860i
37.20	−1.03273	−	1.68526i	−0.743964	−	2.63790i	−0.865588	+	1.69881i	−2.21563	+	0.301644i	−3.67723	+	3.97800i	−1.80598	−	3.22480i	−0.183996	+	0.0144808i	−3.84710	+	2.35751i	2.79649	+	3.42239i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.c	even	5	1	inner
85.r	even	16	1	inner
935.cn	even	80	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	935.2.cn.a	✓	3328
5.c	odd	4	1		935.2.cs.a	yes	3328
11.c	even	5	1	inner	935.2.cn.a	✓	3328
17.e	odd	16	1		935.2.cs.a	yes	3328
55.k	odd	20	1		935.2.cs.a	yes	3328
85.r	even	16	1	inner	935.2.cn.a	✓	3328
187.s	odd	80	1		935.2.cs.a	yes	3328
935.cn	even	80	1	inner	935.2.cn.a	✓	3328

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
935.2.cn.a	✓	3328	1.a	even	1	1	trivial
935.2.cn.a	✓	3328	11.c	even	5	1	inner
935.2.cn.a	✓	3328	85.r	even	16	1	inner
935.2.cn.a	✓	3328	935.cn	even	80	1	inner
935.2.cs.a	yes	3328	5.c	odd	4	1
935.2.cs.a	yes	3328	17.e	odd	16	1
935.2.cs.a	yes	3328	55.k	odd	20	1
935.2.cs.a	yes	3328	187.s	odd	80	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(935, [\chi])\).