Newform orbit 805.2.bm.a

• Label: 805.2.bm.a
• Level: $805$
• Weight: $2$
• Character orbit: 805.bm
• Analytic conductor: $6.428$
• Analytic rank: $0$
• Dimension: $1840$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.bm (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.42795736271\)
Analytic rank:	\(0\)
Dimension:	\(1840\)
Relative dimension:	\(92\) over \(\Q(\zeta_{66})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1840 q - 106 q^{4} - 7 q^{5} - 64 q^{6} - 106 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1	−2.26609	−	1.61368i	−1.03938	−	0.252150i	1.87709	+	5.42348i	−2.19041	+	0.449551i	1.94844	+	2.24862i	1.79946	+	1.93957i	2.93058	−	9.98064i	−1.64978	−	0.850521i	5.68911	+	2.51589i
4.2	−2.19267	−	1.56139i	0.516451	+	0.125290i	1.71572	+	4.95725i	0.283265	−	2.21805i	−0.936780	−	1.08110i	−0.605514	−	2.57553i	2.46148	−	8.38301i	−2.41548	−	1.24527i	−4.08436	+	4.42117i
4.3	−2.14457	−	1.52714i	3.04711	+	0.739220i	1.61289	+	4.66013i	−1.21852	+	1.87489i	−5.40585	−	6.23868i	−1.82387	+	1.91664i	2.17427	−	7.40489i	6.07191	+	3.13029i	5.47642	−	2.15999i
4.4	−2.14120	−	1.52474i	−0.634087	−	0.153828i	1.60576	+	4.63955i	1.06263	+	1.96744i	1.12316	+	1.29619i	−2.62492	−	0.331315i	2.15472	−	7.33831i	−2.28810	−	1.17960i	0.724530	−	5.83291i
4.5	−2.10035	−	1.49565i	2.65945	+	0.645177i	1.52036	+	4.39279i	−0.356049	−	2.20754i	−4.62083	−	5.33272i	2.45909	+	0.976159i	1.92393	−	6.55231i	3.98994	+	2.05696i	−2.55389	+	5.16913i
4.6	−2.09683	−	1.49315i	0.671815	+	0.162980i	1.51308	+	4.37175i	2.06195	+	0.865088i	−1.16533	−	1.34486i	1.97042	+	1.76563i	1.90456	−	6.48632i	−2.24173	−	1.15569i	−3.03185	−	4.89273i
4.7	−2.07834	−	1.47998i	−2.48135	−	0.601969i	1.47502	+	4.26180i	1.07475	−	1.96085i	4.26619	+	4.92345i	−2.60041	+	0.487741i	1.80413	−	6.14430i	3.12823	+	1.61272i	−5.13570	+	2.48471i
4.8	−2.06261	−	1.46878i	−2.49702	−	0.605770i	1.44291	+	4.16902i	2.23126	+	0.146583i	4.26063	+	4.91703i	2.49410	−	0.882871i	1.72044	−	5.85927i	3.20163	+	1.65055i	−4.38692	−	3.57956i
4.9	−2.01598	−	1.43557i	1.62126	+	0.393314i	1.34916	+	3.89815i	0.351570	+	2.20826i	−2.70380	−	3.12035i	0.756558	−	2.53528i	1.48168	−	5.04614i	−0.192708	−	0.0993480i	2.46135	−	4.95650i
4.10	−1.88315	−	1.34098i	−1.92085	−	0.465994i	1.09387	+	3.16053i	−1.97055	−	1.05685i	2.99236	+	3.45337i	0.715301	−	2.54722i	0.875675	−	2.98227i	0.806025	+	0.415535i	2.29361	+	4.63268i
4.11	−1.81390	−	1.29168i	2.56675	+	0.622687i	0.967687	+	2.79595i	2.03763	−	0.920905i	−3.85153	−	4.44490i	−2.57062	−	0.626034i	0.601437	−	2.04830i	3.53396	+	1.82188i	−4.88557	−	0.961522i
4.12	−1.81103	−	1.28963i	0.125596	+	0.0304693i	0.962553	+	2.78111i	−2.21708	−	0.290822i	−0.188165	−	0.217153i	−2.34333	+	1.22833i	0.590651	−	2.01157i	−2.65166	−	1.36703i	3.64014	+	3.38589i
4.13	−1.78677	−	1.27235i	−2.87870	−	0.698364i	0.919523	+	2.65679i	0.00210329	+	2.23607i	4.25500	+	4.91053i	0.135430	+	2.64228i	0.501436	−	1.70773i	5.13268	+	2.64608i	2.84130	−	3.99801i
4.14	−1.77530	−	1.26418i	0.181567	+	0.0440476i	0.899384	+	2.59860i	−0.497482	−	2.18003i	−0.266651	−	0.307731i	−0.708892	+	2.54901i	0.460408	−	1.56801i	−2.63548	−	1.35868i	−1.87277	+	4.49910i
4.15	−1.67727	−	1.19438i	2.19235	+	0.531857i	0.732559	+	2.11659i	−2.20399	−	0.377394i	−3.04192	−	3.51056i	2.56762	−	0.638232i	0.139096	−	0.473716i	1.85700	+	0.957350i	3.24594	+	3.26539i
4.16	−1.63897	−	1.16710i	0.204737	+	0.0496687i	0.669946	+	1.93568i	1.77237	−	1.36334i	−0.277589	−	0.320355i	2.42953	−	1.04757i	0.0274021	−	0.0933231i	−2.62706	−	1.35434i	−4.49602	+	0.165931i
4.17	−1.59935	−	1.13889i	−1.18781	−	0.288159i	0.606704	+	1.75296i	−0.551856	+	2.16690i	1.57154	+	1.81365i	2.15208	−	1.53901i	−0.0802201	+	0.273205i	−1.33865	−	0.690123i	3.35047	−	2.83712i
4.18	−1.57953	−	1.12478i	−1.20006	−	0.291133i	0.575651	+	1.66323i	−1.61616	+	1.54532i	1.56808	+	1.80966i	−2.13998	−	1.55579i	−0.131094	+	0.446466i	−1.31111	−	0.675924i	4.29092	−	0.623055i
4.19	−1.49646	−	1.06563i	2.29446	+	0.556631i	0.449703	+	1.29933i	−1.94366	−	1.10553i	−2.84041	−	3.27801i	−1.91608	−	1.82446i	−0.323507	+	1.10176i	2.28822	+	1.17966i	1.73052	+	3.72559i
4.20	−1.48851	−	1.05996i	1.51488	+	0.367505i	0.437998	+	1.26551i	1.16846	+	1.90649i	−1.86536	−	2.15274i	0.439812	+	2.60894i	−0.340212	+	1.15865i	−0.506719	−	0.261232i	0.281538	−	4.07634i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
7.c	even	3	1	inner
23.c	even	11	1	inner
35.j	even	6	1	inner
115.j	even	22	1	inner
161.m	even	33	1	inner
805.bm	even	66	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	805.2.bm.a	✓	1840
5.b	even	2	1	inner	805.2.bm.a	✓	1840
7.c	even	3	1	inner	805.2.bm.a	✓	1840
23.c	even	11	1	inner	805.2.bm.a	✓	1840
35.j	even	6	1	inner	805.2.bm.a	✓	1840
115.j	even	22	1	inner	805.2.bm.a	✓	1840
161.m	even	33	1	inner	805.2.bm.a	✓	1840
805.bm	even	66	1	inner	805.2.bm.a	✓	1840

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
805.2.bm.a	✓	1840	1.a	even	1	1	trivial
805.2.bm.a	✓	1840	5.b	even	2	1	inner
805.2.bm.a	✓	1840	7.c	even	3	1	inner
805.2.bm.a	✓	1840	23.c	even	11	1	inner
805.2.bm.a	✓	1840	35.j	even	6	1	inner
805.2.bm.a	✓	1840	115.j	even	22	1	inner
805.2.bm.a	✓	1840	161.m	even	33	1	inner
805.2.bm.a	✓	1840	805.bm	even	66	1	inner

Hecke kernels

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