Newform orbit 546.2.u.a

• Label: 546.2.u.a
• Level: $546$
• Weight: $2$
• Character orbit: 546.u
• Analytic conductor: $4.360$
• Analytic rank: $0$
• Dimension: $76$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(4.35983195036\)
Analytic rank:	\(0\)
Dimension:	\(76\)
Relative dimension:	\(38\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
185.1	−0.866025	−	0.500000i	−1.67595	+	0.437249i	0.500000	+	0.866025i	1.40279	+	2.42970i	1.67004	+	0.459307i	1.42569	−	2.22877i		−	1.00000i	2.61763	−	1.46562i		−	2.80557i
185.2	−0.866025	−	0.500000i	−1.59603	+	0.672816i	0.500000	+	0.866025i	1.07511	+	1.86215i	1.71861	+	0.215340i	0.447408	+	2.60765i		−	1.00000i	2.09464	−	2.14767i		−	2.15023i
185.3	−0.866025	−	0.500000i	−1.56696	−	0.737995i	0.500000	+	0.866025i	−1.41378	−	2.44875i	0.988029	+	1.42260i	−2.45899	+	0.976416i		−	1.00000i	1.91073	+	2.31282i			2.82757i
185.4	−0.866025	−	0.500000i	−1.51699	−	0.835899i	0.500000	+	0.866025i	−0.699535	−	1.21163i	0.895807	+	1.48241i	1.97618	+	1.75918i		−	1.00000i	1.60255	+	2.53611i			1.39907i
185.5	−0.866025	−	0.500000i	−1.38893	+	1.03484i	0.500000	+	0.866025i	−1.75377	−	3.03762i	1.72026	−	0.201730i	1.37341	−	2.26136i		−	1.00000i	0.858232	−	2.87462i			3.50754i
185.6	−0.866025	−	0.500000i	−1.18075	−	1.26722i	0.500000	+	0.866025i	0.386492	+	0.669424i	0.388948	+	1.68782i	0.662023	−	2.56159i		−	1.00000i	−0.211678	+	2.99252i		−	0.772984i
185.7	−0.866025	−	0.500000i	−0.685609	+	1.59058i	0.500000	+	0.866025i	−0.587127	−	1.01693i	1.38904	−	1.03468i	−1.73688	+	1.99580i		−	1.00000i	−2.05988	−	2.18103i			1.17425i
185.8	−0.866025	−	0.500000i	−0.266485	+	1.71143i	0.500000	+	0.866025i	0.279399	+	0.483934i	1.08650	−	1.34890i	0.253211	−	2.63361i		−	1.00000i	−2.85797	−	0.912140i		−	0.558798i
185.9	−0.866025	−	0.500000i	−0.219501	−	1.71809i	0.500000	+	0.866025i	0.356048	+	0.616693i	−0.668950	+	1.59766i	−2.23074	−	1.42260i		−	1.00000i	−2.90364	+	0.754242i		−	0.712096i
185.10	−0.866025	−	0.500000i	−0.0864870	−	1.72989i	0.500000	+	0.866025i	−0.886718	−	1.53584i	−0.790045	+	1.54137i	2.61154	+	0.424103i		−	1.00000i	−2.98504	+	0.299226i			1.77344i
185.11	−0.866025	−	0.500000i	0.323515	+	1.70157i	0.500000	+	0.866025i	1.99252	+	3.45115i	0.570612	−	1.63536i	−2.44529	−	1.01022i		−	1.00000i	−2.79068	+	1.10097i		−	3.98504i
185.12	−0.866025	−	0.500000i	0.696855	+	1.58568i	0.500000	+	0.866025i	−1.42622	−	2.47029i	0.189348	−	1.72167i	2.54641	+	0.718201i		−	1.00000i	−2.02879	+	2.20998i			2.85245i
185.13	−0.866025	−	0.500000i	0.804592	−	1.53383i	0.500000	+	0.866025i	2.14723	+	3.71911i	−1.46371	+	0.926039i	2.58099	−	0.581819i		−	1.00000i	−1.70526	−	2.46821i		−	4.29446i
185.14	−0.866025	−	0.500000i	0.896713	−	1.48186i	0.500000	+	0.866025i	−0.277881	−	0.481304i	−1.51751	+	0.834971i	−0.887101	+	2.49260i		−	1.00000i	−1.39181	−	2.65760i			0.555761i
185.15	−0.866025	−	0.500000i	1.11365	−	1.32657i	0.500000	+	0.866025i	−2.12998	−	3.68924i	−1.62773	+	0.592023i	−1.07162	−	2.41901i		−	1.00000i	−0.519589	−	2.95466i			4.25996i
185.16	−0.866025	−	0.500000i	1.30626	+	1.13741i	0.500000	+	0.866025i	−0.604752	−	1.04746i	−0.562548	−	1.63815i	−2.45540	+	0.985399i		−	1.00000i	0.412611	+	2.97149i			1.20950i
185.17	−0.866025	−	0.500000i	1.62717	+	0.593575i	0.500000	+	0.866025i	1.76347	+	3.05441i	−1.11238	−	1.32763i	1.45770	+	2.20797i		−	1.00000i	2.29534	+	1.93169i		−	3.52693i
185.18	−0.866025	−	0.500000i	1.69393	+	0.361382i	0.500000	+	0.866025i	0.0272832	+	0.0472559i	−1.28630	−	1.15993i	2.23165	−	1.42118i		−	1.00000i	2.73881	+	1.22431i		−	0.0545664i
185.19	−0.866025	−	0.500000i	1.72102	−	0.195177i	0.500000	+	0.866025i	0.349437	+	0.605242i	−1.58803	−	0.691481i	−1.78017	−	1.95729i		−	1.00000i	2.92381	−	0.671806i		−	0.698873i
185.20	0.866025	+	0.500000i	−1.72102	−	0.195177i	0.500000	+	0.866025i	−0.349437	−	0.605242i	−1.39286	−	1.02954i	−1.78017	−	1.95729i			1.00000i	2.92381	+	0.671806i		−	0.698873i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
91.m	odd	6	1	inner
273.bf	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.u.a	✓	76
3.b	odd	2	1	inner	546.2.u.a	✓	76
7.d	odd	6	1		546.2.bb.a	yes	76
13.c	even	3	1		546.2.bb.a	yes	76
21.g	even	6	1		546.2.bb.a	yes	76
39.i	odd	6	1		546.2.bb.a	yes	76
91.m	odd	6	1	inner	546.2.u.a	✓	76
273.bf	even	6	1	inner	546.2.u.a	✓	76

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
546.2.u.a	✓	76	1.a	even	1	1	trivial
546.2.u.a	✓	76	3.b	odd	2	1	inner
546.2.u.a	✓	76	91.m	odd	6	1	inner
546.2.u.a	✓	76	273.bf	even	6	1	inner
546.2.bb.a	yes	76	7.d	odd	6	1
546.2.bb.a	yes	76	13.c	even	3	1
546.2.bb.a	yes	76	21.g	even	6	1
546.2.bb.a	yes	76	39.i	odd	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(546, [\chi])\).