Newform orbit 546.2.bi.e

• Label: 546.2.bi.e
• Level: $546$
• Weight: $2$
• Character orbit: 546.bi
• 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.bi (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.

\(\operatorname{Tr}(f)(q) = \) \( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1	−1.00000			−1.66749	+	0.468501i	1.00000			−1.58996	+	0.917964i	1.66749	−	0.468501i	−0.364289	−	2.62055i	−1.00000			2.56101	−	1.56244i	1.58996	−	0.917964i
17.2	−1.00000			−1.40963	−	1.00646i	1.00000			−1.41302	+	0.815806i	1.40963	+	1.00646i	2.62951	+	0.292738i	−1.00000			0.974089	+	2.83745i	1.41302	−	0.815806i
17.3	−1.00000			−1.36360	−	1.06799i	1.00000			2.60318	−	1.50295i	1.36360	+	1.06799i	−2.60776	−	0.446759i	−1.00000			0.718787	+	2.91262i	−2.60318	+	1.50295i
17.4	−1.00000			−1.31411	+	1.12832i	1.00000			1.62172	−	0.936303i	1.31411	−	1.12832i	2.04281	−	1.68135i	−1.00000			0.453768	−	2.96548i	−1.62172	+	0.936303i
17.5	−1.00000			−0.733819	+	1.56892i	1.00000			−3.72094	+	2.14828i	0.733819	−	1.56892i	1.54641	+	2.14677i	−1.00000			−1.92302	−	2.30261i	3.72094	−	2.14828i
17.6	−1.00000			−0.646635	−	1.60682i	1.00000			−2.88000	+	1.66277i	0.646635	+	1.60682i	−2.37914	−	1.15746i	−1.00000			−2.16373	+	2.07805i	2.88000	−	1.66277i
17.7	−1.00000			−0.565041	−	1.63729i	1.00000			1.26448	−	0.730045i	0.565041	+	1.63729i	−1.08820	+	2.41160i	−1.00000			−2.36146	+	1.85028i	−1.26448	+	0.730045i
17.8	−1.00000			−0.436593	+	1.67612i	1.00000			−0.567570	+	0.327687i	0.436593	−	1.67612i	−2.37289	+	1.17020i	−1.00000			−2.61877	−	1.46357i	0.567570	−	0.327687i
17.9	−1.00000			−0.0248275	−	1.73187i	1.00000			−0.511132	+	0.295102i	0.0248275	+	1.73187i	2.62812	−	0.304939i	−1.00000			−2.99877	+	0.0859963i	0.511132	−	0.295102i
17.10	−1.00000			0.787258	+	1.54280i	1.00000			−3.27919	+	1.89324i	−0.787258	−	1.54280i	0.475130	−	2.60274i	−1.00000			−1.76045	+	2.42916i	3.27919	−	1.89324i
17.11	−1.00000			0.805192	−	1.53351i	1.00000			2.64914	−	1.52948i	−0.805192	+	1.53351i	0.969634	−	2.46167i	−1.00000			−1.70333	−	2.46955i	−2.64914	+	1.52948i
17.12	−1.00000			0.841952	+	1.51364i	1.00000			2.84717	−	1.64381i	−0.841952	−	1.51364i	1.87202	+	1.86964i	−1.00000			−1.58223	+	2.54883i	−2.84717	+	1.64381i
17.13	−1.00000			0.929420	−	1.46157i	1.00000			1.09866	−	0.634311i	−0.929420	+	1.46157i	0.151485	+	2.64141i	−1.00000			−1.27236	−	2.71682i	−1.09866	+	0.634311i
17.14	−1.00000			1.21751	−	1.23193i	1.00000			−1.57344	+	0.908426i	−1.21751	+	1.23193i	−2.47008	−	0.947995i	−1.00000			−0.0353243	−	2.99979i	1.57344	−	0.908426i
17.15	−1.00000			1.66045	+	0.492861i	1.00000			1.80315	−	1.04105i	−1.66045	−	0.492861i	−0.800654	−	2.52170i	−1.00000			2.51418	+	1.63674i	−1.80315	+	1.04105i
17.16	−1.00000			1.69024	+	0.378264i	1.00000			−0.870413	+	0.502533i	−1.69024	−	0.378264i	2.64571	−	0.0151415i	−1.00000			2.71383	+	1.27872i	0.870413	−	0.502533i
17.17	−1.00000			1.72971	−	0.0900624i	1.00000			−1.98183	+	1.14421i	−1.72971	+	0.0900624i	−0.877809	+	2.49589i	−1.00000			2.98378	−	0.311563i	1.98183	−	1.14421i
257.1	−1.00000			−1.66749	−	0.468501i	1.00000			−1.58996	−	0.917964i	1.66749	+	0.468501i	−0.364289	+	2.62055i	−1.00000			2.56101	+	1.56244i	1.58996	+	0.917964i
257.2	−1.00000			−1.40963	+	1.00646i	1.00000			−1.41302	−	0.815806i	1.40963	−	1.00646i	2.62951	−	0.292738i	−1.00000			0.974089	−	2.83745i	1.41302	+	0.815806i
257.3	−1.00000			−1.36360	+	1.06799i	1.00000			2.60318	+	1.50295i	1.36360	−	1.06799i	−2.60776	+	0.446759i	−1.00000			0.718787	−	2.91262i	−2.60318	−	1.50295i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
273.br	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.bi.e	✓	34
3.b	odd	2	1		546.2.bi.f	yes	34
7.d	odd	6	1		546.2.bn.f	yes	34
13.e	even	6	1		546.2.bn.e	yes	34
21.g	even	6	1		546.2.bn.e	yes	34
39.h	odd	6	1		546.2.bn.f	yes	34
91.l	odd	6	1		546.2.bi.f	yes	34
273.br	even	6	1	inner	546.2.bi.e	✓	34

    

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

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