Newform orbit 546.2.bn.f

• Label: 546.2.bn.f
• Level: $546$
• Weight: $2$
• Character orbit: 546.bn
• Analytic conductor: $4.360$
• Analytic rank: $0$
• Dimension: $34$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bn (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.35983195036\)
Analytic rank:	\(0\)
Dimension:	\(34\)
Relative dimension:	\(17\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
101.1	0.500000	−	0.866025i	−1.71486	+	0.243407i	−0.500000	−	0.866025i	−2.88000	+	1.66277i	−0.646635	+	1.60682i	−0.187179	−	2.63912i	−1.00000			2.88151	−	0.834819i			3.32554i
101.2	0.500000	−	0.866025i	−1.70046	+	0.329307i	−0.500000	−	0.866025i	1.26448	−	0.730045i	−0.565041	+	1.63729i	−2.63261	+	0.263392i	−1.00000			2.78311	−	1.11994i		−	1.46009i
101.3	0.500000	−	0.866025i	−1.60671	−	0.646913i	−0.500000	−	0.866025i	2.60318	−	1.50295i	−1.36360	+	1.06799i	−0.916975	−	2.48177i	−1.00000			2.16301	+	2.07880i		−	3.00590i
101.4	0.500000	−	0.866025i	−1.57643	−	0.717543i	−0.500000	−	0.866025i	−1.41302	+	0.815806i	−1.40963	+	1.00646i	1.06124	+	2.42359i	−1.00000			1.97026	+	2.26231i			1.63161i
101.5	0.500000	−	0.866025i	−1.51226	+	0.844435i	−0.500000	−	0.866025i	−0.511132	+	0.295102i	−0.0248275	+	1.73187i	1.57814	+	2.12355i	−1.00000			1.57386	−	2.55401i			0.590205i
101.6	0.500000	−	0.866025i	−0.925467	+	1.46407i	−0.500000	−	0.866025i	2.64914	−	1.52948i	0.805192	+	1.53351i	2.61668	−	0.391106i	−1.00000			−1.28702	−	2.70990i		−	3.05896i
101.7	0.500000	−	0.866025i	−0.801045	+	1.53568i	−0.500000	−	0.866025i	1.09866	−	0.634311i	0.929420	+	1.46157i	−2.21179	+	1.45190i	−1.00000			−1.71665	−	2.46030i		−	1.26862i
101.8	0.500000	−	0.866025i	−0.458130	+	1.67036i	−0.500000	−	0.866025i	−1.57344	+	0.908426i	1.21751	+	1.23193i	−0.414054	−	2.61315i	−1.00000			−2.58023	−	1.53049i			1.81685i
101.9	0.500000	−	0.866025i	−0.428009	−	1.67834i	−0.500000	−	0.866025i	−1.58996	+	0.917964i	−1.66749	−	0.468501i	2.08732	−	1.62576i	−1.00000			−2.63362	+	1.43668i			1.83593i
101.10	0.500000	−	0.866025i	0.320103	−	1.70221i	−0.500000	−	0.866025i	1.62172	−	0.936303i	−1.31411	−	1.12832i	2.47749	+	0.928453i	−1.00000			−2.79507	−	1.08977i		−	1.87261i
101.11	0.500000	−	0.866025i	0.786858	+	1.54300i	−0.500000	−	0.866025i	−1.98183	+	1.14421i	1.72971	+	0.0900624i	−2.60041	+	0.487738i	−1.00000			−1.76171	+	2.42825i			2.28842i
101.12	0.500000	−	0.866025i	0.991815	−	1.41997i	−0.500000	−	0.866025i	−3.72094	+	2.14828i	−0.733819	−	1.56892i	−1.08595	+	2.41262i	−1.00000			−1.03261	−	2.81669i			4.29657i
101.13	0.500000	−	0.866025i	1.17271	+	1.27466i	−0.500000	−	0.866025i	−0.870413	+	0.502533i	1.69024	−	0.378264i	1.33597	+	2.28368i	−1.00000			−0.249516	+	2.98961i			1.00507i
101.14	0.500000	−	0.866025i	1.23327	−	1.21616i	−0.500000	−	0.866025i	−0.567570	+	0.327687i	−0.436593	−	1.67612i	−2.19987	−	1.46989i	−1.00000			0.0419009	−	2.99971i			0.655374i
101.15	0.500000	−	0.866025i	1.25705	+	1.19156i	−0.500000	−	0.866025i	1.80315	−	1.04105i	1.66045	−	0.492861i	1.78353	−	1.95424i	−1.00000			0.160371	+	2.99571i		−	2.08210i
101.16	0.500000	−	0.866025i	1.72973	−	0.0896134i	−0.500000	−	0.866025i	−3.27919	+	1.89324i	0.787258	−	1.54280i	2.49160	−	0.889895i	−1.00000			2.98394	−	0.310014i			3.78649i
101.17	0.500000	−	0.866025i	1.73183	−	0.0276700i	−0.500000	−	0.866025i	2.84717	−	1.64381i	0.841952	−	1.51364i	−0.683149	+	2.55603i	−1.00000			2.99847	−	0.0958395i		−	3.28763i
173.1	0.500000	+	0.866025i	−1.71486	−	0.243407i	−0.500000	+	0.866025i	−2.88000	−	1.66277i	−0.646635	−	1.60682i	−0.187179	+	2.63912i	−1.00000			2.88151	+	0.834819i		−	3.32554i
173.2	0.500000	+	0.866025i	−1.70046	−	0.329307i	−0.500000	+	0.866025i	1.26448	+	0.730045i	−0.565041	−	1.63729i	−2.63261	−	0.263392i	−1.00000			2.78311	+	1.11994i			1.46009i
173.3	0.500000	+	0.866025i	−1.60671	+	0.646913i	−0.500000	+	0.866025i	2.60318	+	1.50295i	−1.36360	−	1.06799i	−0.916975	+	2.48177i	−1.00000			2.16301	−	2.07880i			3.00590i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
273.y	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	546.2.bn.f	yes	34
3.b	odd	2	1		546.2.bn.e	yes	34
7.d	odd	6	1		546.2.bi.e	✓	34
13.e	even	6	1		546.2.bi.f	yes	34
21.g	even	6	1		546.2.bi.f	yes	34
39.h	odd	6	1		546.2.bi.e	✓	34
91.p	odd	6	1		546.2.bn.e	yes	34
273.y	even	6	1	inner	546.2.bn.f	yes	34

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
546.2.bi.e	✓	34	7.d	odd	6	1
546.2.bi.e	✓	34	39.h	odd	6	1
546.2.bi.f	yes	34	13.e	even	6	1
546.2.bi.f	yes	34	21.g	even	6	1
546.2.bn.e	yes	34	3.b	odd	2	1
546.2.bn.e	yes	34	91.p	odd	6	1
546.2.bn.f	yes	34	1.a	even	1	1	trivial
546.2.bn.f	yes	34	273.y	even	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^34 + 9*T5^33 - 10*T5^32 - 333*T5^31 - 234*T5^30 + 7575*T5^29 + 13479*T5^28 - 110490*T5^27 - 271152*T5^26 + 1182456*T5^25 + 3657921*T5^24 - 8992971*T5^23 - 34473685*T5^22 + 49725264*T5^21 + 246076879*T5^20 - 173123175*T5^19 - 1305032778*T5^18 + 264077631*T5^17 + 5315188447*T5^16 + 1176675570*T5^15 - 15985729585*T5^14 - 9008789877*T5^13 + 35852408112*T5^12 + 33168119847*T5^11 - 53535398844*T5^10 - 72810204549*T5^9 + 49496707143*T5^8 + 111362033196*T5^7 - 439013472*T5^6 - 93732114042*T5^5 - 38492559526*T5^4 + 44638970124*T5^3 + 51885957901*T5^2 + 20997409461*T5 + 3270763083