Newform orbit 805.2.bn.a

• Label: 805.2.bn.a
• Level: $805$
• Weight: $2$
• Character orbit: 805.bn
• 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.bn (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.

\(\operatorname{Tr}(f)(q) = \) \( 1840 q - 106 q^{4} - 33 q^{5} + 62 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−0.264785	+	2.77296i	1.63686	+	1.56074i	−5.65532	−	1.08997i	0.153930	−	2.23076i	−4.76128	+	4.12568i	−1.58844	−	2.11586i	2.95032	−	10.0479i	0.100646	+	2.11282i	6.14505	+	1.01751i
19.2	−0.261867	+	2.74240i	0.897342	+	0.855613i	−5.48833	−	1.05779i	1.60597	+	1.55591i	−2.58142	+	2.23681i	2.52453	+	0.791682i	2.78582	−	9.48763i	−0.0695983	−	1.46105i	−4.68749	+	3.99677i
19.3	−0.260814	+	2.73137i	−1.51415	−	1.44374i	−5.42849	−	1.04626i	2.18347	−	0.482147i	4.33831	−	3.75916i	−2.46173	+	0.969468i	2.72751	−	9.28904i	0.0655230	+	1.37550i	0.747442	+	6.08961i
19.4	−0.245186	+	2.56770i	−1.10596	−	1.05453i	−4.56911	−	0.880624i	−0.544158	+	2.16885i	2.97889	−	2.58122i	−0.652547	−	2.56402i	1.92807	−	6.56639i	−0.0316328	−	0.664054i	−5.43553	−	1.92900i
19.5	−0.244059	+	2.55590i	0.237653	+	0.226602i	−4.50920	−	0.869076i	−1.88592	+	1.20138i	−0.637173	+	0.552113i	2.14701	+	1.54608i	1.87507	−	6.38590i	−0.137615	−	2.88890i	−2.61032	−	5.11343i
19.6	−0.237841	+	2.49078i	−0.0677744	−	0.0646228i	−4.18357	−	0.806316i	−2.10236	−	0.761621i	0.177081	−	0.153441i	−2.38510	+	1.14511i	1.59353	−	5.42706i	−0.142328	−	2.98784i	2.39706	−	5.05538i
19.7	−0.233885	+	2.44936i	−2.40125	−	2.28958i	−3.98079	−	0.767235i	−2.22380	+	0.233941i	6.16963	−	5.34601i	−0.0364833	+	2.64550i	1.42388	−	4.84928i	0.381045	+	7.99912i	−0.0528928	−	5.50159i
19.8	−0.227761	+	2.38522i	2.24104	+	2.13683i	−3.67353	−	0.708015i	1.66810	+	1.48910i	−5.60722	+	4.85869i	−1.26138	+	2.32571i	1.17536	−	4.00290i	0.313484	+	6.58084i	−3.93176	+	3.63963i
19.9	−0.223414	+	2.33970i	−2.07114	−	1.97483i	−3.46042	−	0.666941i	1.32814	+	1.79890i	5.08323	−	4.40464i	2.64575	−	0.00333524i	1.00921	−	3.43707i	0.246929	+	5.18369i	−4.50561	+	2.70556i
19.10	−0.221173	+	2.31622i	2.33565	+	2.22703i	−3.35212	−	0.646069i	−2.22966	−	0.169212i	−5.67489	+	4.91732i	2.56293	+	0.656794i	0.926789	−	3.15635i	0.352816	+	7.40652i	0.885073	−	5.12696i
19.11	−0.218341	+	2.28658i	0.597879	+	0.570076i	−3.21690	−	0.620006i	2.15535	−	0.595359i	−1.43406	+	1.24262i	1.74948	−	1.98477i	0.825807	−	2.81244i	−0.110274	−	2.31493i	0.890729	+	5.05837i
19.12	−0.218140	+	2.28447i	0.490631	+	0.467816i	−3.20735	−	0.618166i	0.718809	+	2.11738i	−1.17574	+	1.01878i	−2.64216	+	0.137843i	0.818760	−	2.78844i	−0.120878	−	2.53755i	−4.99390	+	1.18021i
19.13	−0.212949	+	2.23010i	1.68653	+	1.60810i	−2.96414	−	0.571292i	0.576523	−	2.16047i	−3.94536	+	3.41868i	−0.388742	+	2.61704i	0.642949	−	2.18968i	0.115641	+	2.42759i	4.69529	+	1.74577i
19.14	−0.209075	+	2.18953i	−0.384524	−	0.366643i	−2.78648	−	0.537049i	0.427391	−	2.19484i	0.883170	−	0.765271i	0.238318	+	2.63500i	0.519131	−	1.76800i	−0.129314	−	2.71464i	4.71632	+	1.39467i
19.15	−0.204675	+	2.14346i	−1.05338	−	1.00439i	−2.58866	−	0.498923i	1.70146	−	1.45088i	2.36847	−	2.05229i	−0.297394	−	2.62898i	0.385998	−	1.31459i	−0.0419480	−	0.880597i	2.76165	+	3.94396i
19.16	−0.204085	+	2.13727i	−2.07442	−	1.97796i	−2.56243	−	0.493867i	−1.14433	−	1.92107i	4.65079	−	4.02993i	−0.765172	−	2.53269i	0.368724	−	1.25576i	0.248165	+	5.20962i	4.33939	−	2.05368i
19.17	−0.187302	+	1.96152i	1.52585	+	1.45489i	−1.84862	−	0.356292i	−2.17383	+	0.523901i	−3.13960	+	2.72048i	−2.15183	−	1.53935i	−0.0651514	+	0.221885i	0.0687525	+	1.44329i	−0.620480	−	4.36213i
19.18	−0.179747	+	1.88239i	−1.06787	−	1.01821i	−1.54723	−	0.298205i	−1.65593	+	1.50262i	2.10861	−	1.82712i	2.18318	−	1.49456i	−0.226038	+	0.769816i	−0.0391557	−	0.821980i	−2.53088	−	3.38721i
19.19	−0.177738	+	1.86136i	0.853467	+	0.813779i	−1.46921	−	0.283167i	−1.69457	−	1.45892i	−1.66643	+	1.44397i	1.11225	−	2.40061i	−0.265372	+	0.903774i	−0.0765763	−	1.60753i	3.01676	−	2.89489i
19.20	−0.176009	+	1.84325i	−0.913793	−	0.871299i	−1.40274	−	0.270355i	2.19608	+	0.421004i	1.76686	−	1.53099i	1.06695	+	2.42108i	−0.298105	+	1.01525i	−0.0668916	−	1.40423i	−1.16255	+	3.97382i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
7.d	odd	6	1	inner
23.d	odd	22	1	inner
35.i	odd	6	1	inner
115.i	odd	22	1	inner
161.o	even	66	1	inner
805.bn	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.bn.a	✓	1840
5.b	even	2	1	inner	805.2.bn.a	✓	1840
7.d	odd	6	1	inner	805.2.bn.a	✓	1840
23.d	odd	22	1	inner	805.2.bn.a	✓	1840
35.i	odd	6	1	inner	805.2.bn.a	✓	1840
115.i	odd	22	1	inner	805.2.bn.a	✓	1840
161.o	even	66	1	inner	805.2.bn.a	✓	1840
805.bn	even	66	1	inner	805.2.bn.a	✓	1840

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
805.2.bn.a	✓	1840	1.a	even	1	1	trivial
805.2.bn.a	✓	1840	5.b	even	2	1	inner
805.2.bn.a	✓	1840	7.d	odd	6	1	inner
805.2.bn.a	✓	1840	23.d	odd	22	1	inner
805.2.bn.a	✓	1840	35.i	odd	6	1	inner
805.2.bn.a	✓	1840	115.i	odd	22	1	inner
805.2.bn.a	✓	1840	161.o	even	66	1	inner
805.2.bn.a	✓	1840	805.bn	even	66	1	inner

Hecke kernels

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