Newform orbit 805.2.bs.a

• Label: 805.2.bs.a
• Level: $805$
• Weight: $2$
• Character orbit: 805.bs
• Analytic conductor: $6.428$
• Analytic rank: $0$
• Dimension: $3680$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.bs (of order \(132\), degree \(40\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.42795736271\)
Analytic rank:	\(0\)
Dimension:	\(3680\)
Relative dimension:	\(92\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8}+O(q^{10}) \)

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	−2.37524	+	1.44778i	0.0889339	+	0.183078i	2.62922	−	5.09998i	−1.40279	−	1.74131i	−0.476296	−	0.306097i	1.44280	+	2.21773i	0.741747	+	10.3710i	1.82887	−	2.32560i	5.85301	+	2.10509i
37.2	−2.30557	+	1.40532i	−1.13353	−	2.33346i	2.42427	−	4.70243i	−0.533908	+	2.17139i	5.89267	+	3.78699i	−0.0145566	+	2.64571i	0.633836	+	8.86218i	−2.30569	+	2.93193i	−1.82053	−	5.75660i
37.3	−2.26511	+	1.38065i	1.14262	+	2.35218i	2.30804	−	4.47698i	1.24242	+	1.85914i	−5.83570	−	3.75038i	−1.39693	−	2.24691i	0.574713	+	8.03553i	−2.37270	+	3.01713i	−5.38104	−	2.49578i
37.4	−2.24779	+	1.37010i	0.546593	+	1.12521i	2.25894	−	4.38172i	2.23051	−	0.157581i	−2.77028	−	1.78035i	−1.70764	+	2.02089i	0.550193	+	7.69270i	0.887145	−	1.12810i	−4.79781	+	3.41023i
37.5	−2.22577	+	1.35668i	−0.128329	−	0.264176i	2.19703	−	4.26165i	−2.05851	+	0.873231i	0.644033	+	0.413895i	−1.75315	−	1.98153i	0.519683	+	7.26612i	1.80116	−	2.29036i	3.39708	−	4.73635i
37.6	−2.22496	+	1.35619i	1.31748	+	2.71216i	2.19477	−	4.25726i	−2.13549	+	0.663098i	−6.60955	−	4.24770i	2.64575	+	0.00158949i	0.518576	+	7.25065i	−3.76556	+	4.78829i	3.85210	−	4.37149i
37.7	−2.19061	+	1.33525i	−1.35414	−	2.78762i	2.09945	−	4.07236i	0.904680	−	2.04488i	6.68858	+	4.29849i	−2.20529	−	1.46175i	0.472496	+	6.60636i	−4.08266	+	5.19152i	0.748626	+	5.68753i
37.8	−2.08232	+	1.26924i	0.0668818	+	0.137682i	1.80864	−	3.50827i	0.447044	−	2.19092i	−0.314021	−	0.201809i	0.109828	−	2.64347i	0.338730	+	4.73606i	1.83999	−	2.33974i	1.84992	+	5.12962i
37.9	−2.03883	+	1.24273i	0.879859	+	1.81127i	1.69598	−	3.28975i	1.72696	−	1.42043i	−4.04479	−	2.59943i	1.66548	−	2.05577i	0.289777	+	4.05161i	−0.652056	+	0.829157i	−1.75576	+	5.04215i
37.10	−1.96942	+	1.20042i	−1.19833	−	2.46688i	1.52115	−	2.95061i	−2.19848	−	0.408248i	5.32132	+	3.41981i	2.13293	−	1.56544i	0.217132	+	3.03590i	−2.79499	+	3.55412i	4.81981	−	1.83510i
37.11	−1.96536	+	1.19795i	−0.713439	−	1.46868i	1.51109	−	2.93111i	1.59357	+	1.56861i	3.16156	+	2.03181i	−2.41121	−	1.08907i	0.213081	+	2.97927i	0.206463	−	0.262539i	−5.01104	−	1.17387i
37.12	−1.90357	+	1.16029i	−0.663296	−	1.36545i	1.36087	−	2.63972i	2.13191	−	0.674517i	2.84695	+	1.82963i	2.60528	+	0.460985i	0.154245	+	2.15663i	0.429976	−	0.546759i	−3.27561	+	3.75762i
37.13	−1.89442	+	1.15471i	0.806631	+	1.66052i	1.33901	−	2.59732i	−1.78921	−	1.34116i	−3.44551	−	2.21430i	−2.54843	+	0.710975i	0.145954	+	2.04070i	−0.252199	+	0.320697i	4.93817	+	0.474704i
37.14	−1.88830	+	1.15098i	−0.812204	−	1.67199i	1.32447	−	2.56911i	0.424637	−	2.19538i	3.45811	+	2.22240i	0.926181	+	2.47834i	0.140475	+	1.96410i	−0.281410	+	0.357843i	1.72499	+	4.63428i
37.15	−1.88161	+	1.14690i	−0.180822	−	0.372238i	1.30862	−	2.53836i	−0.543974	+	2.16889i	0.767156	+	0.493021i	2.09714	−	1.61308i	0.134538	+	1.88109i	1.74861	−	2.22354i	−1.46396	−	4.70489i
37.16	−1.85265	+	1.12925i	1.44589	+	2.97649i	1.24065	−	2.40653i	0.806258	−	2.08565i	−6.03992	−	3.88162i	−0.440107	+	2.60889i	0.109510	+	1.53114i	−4.91443	+	6.24921i	0.861507	+	4.77444i
37.17	−1.75718	+	1.07105i	−0.388807	−	0.800393i	1.02406	−	1.98639i	1.91892	+	1.14793i	1.54047	+	0.989998i	−1.91797	+	1.82247i	0.0344743	+	0.482013i	1.36502	−	1.73576i	−4.60138	+	0.0381534i
37.18	−1.59878	+	0.974510i	0.214397	+	0.441355i	0.689990	−	1.33839i	−1.58263	+	1.57964i	−0.772880	−	0.496700i	−0.922277	+	2.47980i	−0.0660143	−	0.923000i	1.70565	−	2.16891i	0.990910	−	4.06780i
37.19	−1.52376	+	0.928783i	−0.164334	−	0.338297i	0.542767	−	1.05282i	−2.23602	−	0.0147772i	0.564611	+	0.362854i	1.55128	+	2.14325i	−0.103819	−	1.45157i	1.76704	−	2.24697i	3.42089	−	2.05426i
37.20	−1.47228	+	0.897400i	1.05789	+	2.17776i	0.445823	−	0.864775i	−1.05740	+	1.97026i	−3.51183	−	2.25691i	−2.36683	−	1.18243i	−0.126334	−	1.76638i	−1.76902	+	2.24949i	−0.211323	−	3.84967i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
7.c	even	3	1	inner
23.d	odd	22	1	inner
35.l	odd	12	1	inner
115.l	even	44	1	inner
161.p	odd	66	1	inner
805.bs	even	132	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	805.2.bs.a	✓	3680
5.c	odd	4	1	inner	805.2.bs.a	✓	3680
7.c	even	3	1	inner	805.2.bs.a	✓	3680
23.d	odd	22	1	inner	805.2.bs.a	✓	3680
35.l	odd	12	1	inner	805.2.bs.a	✓	3680
115.l	even	44	1	inner	805.2.bs.a	✓	3680
161.p	odd	66	1	inner	805.2.bs.a	✓	3680
805.bs	even	132	1	inner	805.2.bs.a	✓	3680

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
805.2.bs.a	✓	3680	1.a	even	1	1	trivial
805.2.bs.a	✓	3680	5.c	odd	4	1	inner
805.2.bs.a	✓	3680	7.c	even	3	1	inner
805.2.bs.a	✓	3680	23.d	odd	22	1	inner
805.2.bs.a	✓	3680	35.l	odd	12	1	inner
805.2.bs.a	✓	3680	115.l	even	44	1	inner
805.2.bs.a	✓	3680	161.p	odd	66	1	inner
805.2.bs.a	✓	3680	805.bs	even	132	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(805, [\chi])\).